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Currently, two-dimensional dyadic wavelet transform (2D-DWT) is habitually considered as the one presented by Mallat, which is defined by an approximation component, two detail components in horizontal and vertical directions. This paper is to introduce a new type of two-dimensional dyadic wavelet transform and its application so that dyadic wavelet can be studied and used widely furthermore. (1) Two-dimensional stationary dyadic wavelet transform (2D-SDWT) is proposed, it is defined by approximation coefficients, detail coefficients in horizontal, vertical and diagonal directions, which is essentially the extension of two-dimensional stationary wavelet transform for orthogonal/biorthogonal wavelet filters. (2) ε-decimated dyadic discrete wavelet transform (DDWT) is introduced and its relation with 2D-SDWT is given, where ε is a sequence of 0's and 1's. (3) Mallat decomposition algorithm based on dyadic wavelet is introduced as a special case of ε-decimated DDWT, and so a face recognition algorithm based on dyadic wavelet is proposed, and experimental results are given to show its effectiveness. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Gröbner bases via Buchberger’s Algorithm. In a nutshell, the idea is to extend the advantages of computing with homogeneous polynomials or vectors to the general case. When the input data are not homogeneous, we use as a main tool the procedure of a self-saturating Buchberger’s Algorithm. Another strictly related topic is treated later when a mathematical foundation is given to the sugar trick which is nowadays widely used in most of the implementations of Buchberger’s Algorithm. A special emphasis is also given to the case of a single grading, and subsequently some timings and indicators showing the practical merits of our approach. [Copyright &y& Elsevier]

Abstract: The paper focuses on the numerical study of electromagnetic scattering from two-dimensional (2D) large partly covered cavities, which is described by the Helmholtz equation with a nonlocal boundary condition on the aperture. The classical five-point finite difference method is applied for the discretization of the Helmholtz equation and a linear approximation is used for the nonlocal boundary condition. We prove the existence and uniqueness of the numerical solution when the medium in the cavity is -direction layered or the number of the mesh points on the aperture is large enough. The fast algorithm proposed in Bao and Sun (2005) for open cavity models is extended to solving the partly covered cavity problem with (vertically) layered media. A preconditioned Krylov subspace method is proposed to solve the partly covered cavity problem with a general medium, in which a layered medium model is used as a preconditioner of the general model. Numerical results for several types of partly covered cavities with different wave numbers are reported and compared with those by ILU-type preconditioning algorithms. Our numerical experiments show that the proposed preconditioning algorithm is more efficient for partly covered cavity problems, particularly with large wave numbers. [Copyright &y& Elsevier]

Abstract: Image representation by using polynomial moments is an interesting theme. In this paper, image representation by using orthogonal Gegenbauer function is presented. A novel method for accurate and fast computation of orthogonal Gegenbauer moments is proposed. The accurate values of Gegenbauer moments are obtained by mathematically integrating Gegenbauer polynomials multiplied by their weight functions over the digital image pixels. A novel recurrence formula is derived for the kernel generation. The proposed method removes the numerical approximation errors involved in conventional method. A fast algorithm is proposed to accelerate the moment’s computations. A comparison with the conventional method is performed. The obtained results explain the efficiency and the superiority of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper the identification of Boolean control networks is addressed. First, necessary and sufficient conditions are obtained for the identification of state equation from input-state data. Then a necessary and sufficient condition for a controllable Boolean network to be observable is presented. Based on these two results, a necessary and sufficient condition for the identification from input–output data is achieved. To practically identify the model, a numerical algorithm is proposed. Two particular cases: (i) identification of systems with a known network graph; (ii) identification of a higher order Boolean network, are also investigated. Finally, the approximate identification for large size networks is explored. [Copyright &y& Elsevier]

We study the waiting-time distributions in cyclic polling models with renewal arrivals, general service and switch-over times, and exhaustive service at each of the queues. The assumption of renewal arrivals prohibits an exact analysis and reduces the available analytic results to heavy-traffic asymptotics, limiting results for large switch-over times and large numbers of queues, and some numerical algorithms. Motivated by this, the goal of this paper is to propose a new method for deriving simple closed-form approximations for the complete waiting-time distributions that work well for arbitrary load values. Extensive simulation results show that the approximations are highly accurate over a wide range of parameter settings. [ABSTRACT FROM AUTHOR]

The goal of this paper is to solve mathematical model equations on solid tumour growth and compute their parameter values by applying growth rates of prostate cancer cell lines in vivo. For these computations, we investigate previously developed C3(1)/Tag transgenic models of prostate cancer. To make the computations fast, we have constructed an algorithm, which is based on small amounts of spatial grid-points and obtained a correspondence between the in vivo growth of tumours and the solutions of the model equations. [ABSTRACT FROM AUTHOR]

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly nonsmooth) regularizer is minimized under the constraint that the solution explains the observations sufficiently well. Although the regularizer and constraint are usually convex, several particular features of these problems (huge dimensionality, nonsmoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications. The proposed algorithm, which belongs to the family of augmented Lagrangian methods, can be used to deal with a variety of imaging IPLIP, including deconvolution and reconstruction from compressive observations (such as MRI), using either total-variation or wavelet-based (or, more generally, frame-based) regularization. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence sufficient conditions are known; we show that these conditions are satisfied by the proposed algorithm. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is a strong contender for the state-of-the-art. [ABSTRACT FROM AUTHOR]

Abstract: The variational iteration method and the homotopy analysis method, as alternative methods, have been widely used to handle linear and nonlinear models. The main property of the methods is their flexibility and ability to solve nonlinear equations accurately and conveniently. This paper deals with the numerical solutions of nonlinear fractional differential equations, where the fractional derivatives are considered in Caputo sense. The main aim is to introduce efficient algorithms of variational iteration and homotopy analysis methods that can be simply used to deal with nonlinear fractional differential equations. In these algorithms, Legendre polynomials are effectively implemented to achieve better approximation for the nonhomogeneous and nonlinear terms that leads to facilitate the computational work. The proposed algorithms are capable of reducing the size of calculations, improving the accuracy and easily overcome the difficulty arising in calculating complicated integrals. Numerical examples are examined to show the efficiency of the algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, we present an new approach to construct the so-called shape preserving interpolation curves. The basic idea is first to approximate the set of interpolated points with a class of MQ quasi-interpolation operators and then pass through the set with the use of multivariate interpolation by using compactly supported radial basis functions. This approach possesses the advantages of certain shape preserving and good approximation behaviors. The proposed algorithm is easy to implement. [Copyright &y& Elsevier]

Abstract: Symmetric rank-one (SR1) is one of the competitive formulas among the quasi-Newton (QN) methods. In this paper, we propose some modified SR1 updates based on the modified secant equations, which use both gradient and function information. Furthermore, to avoid the loss of positive definiteness and zero denominators of the new SR1 updates, we apply a restart procedure to this update. Three new algorithms are given to improve the Hessian approximation with modified secant equations for the SR1 method. Numerical results show that the proposed algorithms are very encouraging and the advantage of the proposed algorithms over the standard SR1 and BFGS updates is clearly observed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present stabilized finite element methods to discretize in space the monochromatic radiation transport equation. These methods are based on the decomposition of the unknowns into resolvable and subgrid scales, with an approximation for the latter that yields a problem to be solved for the former. This approach allows us to design the algorithmic parameters on which the method depends, which we do here when the discrete ordinates method is used for the directional approximation. We concentrate on two stabilized methods, namely, the classical SUPG technique and the orthogonal subscale stabilization. A numerical analysis of the spatial approximation for both formulations is performed, which shows that they have a similar behavior: they are both stable and optimally convergent in the same mesh-dependent norm. A comparison with the behavior of the Galerkin method, for which a non-standard numerical analysis is done, is also presented. [ABSTRACT FROM AUTHOR]

A new algorithm is developed for computing etAB, where A is an n x n matrix and B is n x n0 with n0 « n. The algorithm works for any A, its computational cost is dominated by the formation of products of A with n x n0 matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix etA B or a sequence Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. on an equally spaced grid of points tk. It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. It determines the amount of scaling and the Taylor degree, using the recent analysis of Al-Mohy and Higham [SIAM J. Matrix Anal. Appl., 31 (2009), pp. 970 989], which provides sharp truncation error bounds expressed in terms of the quantities ||Ak

Abstract: A recurring task in image processing, approximation theory, and the numerical solution of partial differential equations is to reconstruct a piecewise-smooth real-valued function , where , from its truncated Fourier transform (its truncated spectrum). An essential step is edge detection for which a variety of one-dimensional schemes have been developed over the last few decades. Most higher-dimensional edge detection algorithms consist of applying one-dimensional detectors in each component direction in order to recover the locations in where is singular (the singular support). In this paper, we present a multidimensional algorithm which identifies the wavefront of a function from spectral data. The wavefront of f is the set of points which encode both the location of the singular points of a function and the orientation of the singularities. (Here denotes the unit sphere in N dimensions.) More precisely, is the direction of the normal line to the curve or surface of discontinuity at x. Note that the singular support is simply the projection of the wavefront onto its x-component. In one dimension, the wavefront is a subset of , and it coincides with the singular support. In higher dimensions, geometry comes into play and they are distinct. We discuss the advantages of wavefront reconstruction and indicate how it can be used for segmentation in magnetic resonance imaging (MRI). [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a nonlinear stationary Stokes problem with mixed boundary conditions that describes the ice velocity and pressure fields of grounded glaciers under Glen's flow law. Using convex analysis arguments, we prove the existence and the uniqueness of a weak solution. A finite element method is applied with approximation spaces that satisfy the inf-sup condition, and a priori error estimates are established by using a quasinorm technique. Several algorithms including Newton's method are proposed to solve the nonlinearity of the Stokes problem and are proved to be convergent. Our results are supported by numerical convergence studies. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a new method of investigating the change of dynamics in reaction–diffusion equations, which is based on approximating the Euclidian norm of state variables along with the introduction of phase space. Our method is simple in implementation and can be applied to study the dynamics of multiple spirals. The method is extended to study the stability of spiral waves by developing an algorithm which is applied to circular and meandering motions. [Copyright &y& Elsevier]

Abstract: This work is concerned with several properties of solutions of stochastic differential equations arising from hybrid switching diffusions. The word “hybrid” highlights the coexistence of continuous dynamics and discrete events. The underlying process has two components. One component describes the continuous dynamics, whereas the other is a switching process representing discrete events. One of the main features is the switching component depending on the continuous dynamics. In this paper, weak continuity is proved first. Then continuous and smooth dependence on initial data are demonstrated. In addition, it is shown that certain functions of the solutions verify a system of Kolmogorov''s backward differential equations. Moreover, rates of convergence of numerical approximation algorithms are dealt with. [Copyright &y& Elsevier]

In this paper we proposed quasi-Newton and limited memory quasi-Newton methods for objective functions defined ell Grassmannians or a product of Grassmannians. Specifically we defined BFGS and limited memory BFGS updates in local and global coordinates oil Grassmannians or a product, of these. We proved that, when local coordinates are used, our BFGS updates on Grassmaunians share the same optimality property as the usual BFGS updates on Euclidean spaces. When applied to the best multilinear rank approximation problem for general and symmetric tensors, our approach yields fast, robust, and accurate algorithms that exploit the special Grassmannian structure of the respective problems and which work on tensors of large dimensions and arbitrarily high order. Extensive numerical experiments are included to substantiate our claims. [ABSTRACT FROM AUTHOR]

Abstract: Let R and S be m × m and n × n nontrivial real symmetric involutions. An m × n complex matrix A is termed (R, S)-conjugate if , where denotes the conjugate of A. In this paper, necessary and sufficient conditions are established for the existence of the (R, S)-conjugate solution to the system of matrix equations AX = C and XB = D. The expression is also presented for such solution to this system. In addition, the explicit expression of this solution to the corresponding optimal approximation problem is obtained. Furthermore, the least squares (R, S)-conjugate solution with least norm to this system mentioned above is considered. The representation of such solution is also derived. Finally an algorithm and numerical examples are given. [ABSTRACT FROM AUTHOR]

Abstract: This paper solves the multi-layer multiple-scattering plane-parallel radiative transfer problem for solar and thermal sources. Efficient calculation of radiances for optically thin media is made possible by the method herein called PARTM—“Padé approximation radiative transfer method”. The algorithm calculates the matrix exponential and the global reflection and transmission operators using Padé approximants with an accuracy prescribed by the user. In a multi-layer atmosphere, these operators can be combined using the adding method. Computational gain is enhanced by exploiting the symmetry inherent in the exponential solution and then exploiting the structure of this matrix to halve the order of the matrix solution. A range of numerical tests were performed that demonstrate the accuracy and speed of PARTM relative to widely used DISORT model. Finally, the method was applied for two example cases, one for a multispectral instrument such MODIS and one for an instrument similar to the GOSAT and OCO O2 A-band spectrometers. [Copyright &y& Elsevier]

Abstract: For nonsmooth convex optimization, Robert Mifflin and Claudia Sagastizábal introduce a -space decomposition algorithm in Mifflin and Sagastizábal (2005) . An attractive property of this algorithm is that if a primal–dual track exists, this algorithm uses a bundle subroutine. With the inclusion of a simple line search, it is proved to be globally and superlinearly convergent. However, a drawback is that it needs the exact subgradients of the objective function, which is expensive to compute. In this paper an approximate decomposition algorithm based on proximal bundle-type method is introduced that is capable to deal with approximate subgradients. It is shown that the sequence of iterates generated by the resulting algorithm converges to the optimal solutions of the problem. Numerical tests emphasize the theoretical findings. [Copyright &y& Elsevier]

Abstract: In this paper, by solving the relaxed quasiconcave programming problem in outcome space, a new global optimization algorithm for convex multiplicative programming is presented. Two kinds of techniques are employed to establish the algorithm. The first one is outer approximation technique which is applied to shrink relaxation area of quasiconcave programming problem and to compute appropriate feasible points and to raise the capacity of bounding. And the other one is branch and bound technique which is used to guarantee global optimization. Some numerical results are presented to demonstrate the effectiveness and feasibility of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper presents an inelastic element for the analysis of beams resting on two-parameter foundations. The element is derived from a two field mixed formulation with independent approximation of forces and displacements. The values for the two parameters of the foundation are derived through an iterative technique that is based on an assumption of plane strain for the soil medium. This iterative behavior is repeated at each time step of the nonlinear solution algorithm. The nonlinear response of structures resting on this improved two-parameter foundation model is analyzed following both a Vlasov and a Pasternak approach. Numerical examples that clarify the advantage of the newly developed model are conducted. These studies confirmed the importance of accounting for the foundation second parameter, and the efficiency and accuracy of the proposed model. [Copyright &y& Elsevier]

Abstract  In this paper, we study and formulate a BP learning algorithm for fuzzy relational neural networks based on smooth fuzzy norms for functions approximation. To elaborate the model behavior more, we have used different fuzzy norms led to a new pair of fuzzy norms. An important practical case in fuzzy relational equations (FREs) is the identification problem which is studied in this work. In this work we employ a neuro-based approach to numerically solve the set of FREs and focus on generalized neurons that use smooth s-norms and t-norms as fuzzy compositional operators. [ABSTRACT FROM AUTHOR]

Abstract: Computer modeling of radiation deep penetration problems is historically based on the discrete ordinates (S N) formulation. For efficiency reasons, besides accuracy, coarse-mesh spatial discretization is desirable. The spectral Green''s function (SGF) methods form a class of accurate coarse-mesh numerical methods as they use polynomial approximations only for the node-edge transverse leakage terms; the scattering source terms are treated analytically in the numerical algorithm. Therefore, algebraic work and the computational algorithms of the spectral nodal methods are rather complicated. To alleviate this negative feature, we offer in this paper a composite spatial grid SGF nodal method for the numerical solution of one-speed deep penetration S N problems with isotropic scattering in X,Y geometry. This method uses a rectangular coarse spatial grid, that is coincident with the material region distribution within the shielding structure. We first transverse integrate the S N equations separately in the x- and y-coordinate directions inside each material region, and then we introduce flat approximations for the transverse leakage terms. Furthermore, we use a fine spatial grid to discretize each set of “one-dimensional”S N nodal equations. As the spatial directions are coupled by the transverse leakage terms, we use an explicit alternate direction technique to converge the numerical solution. In order to verify the offered method''s accuracy, we present numerical results for typical model problems. Moreover, we compare the computing performance of this method with the conventional SGF-constant nodal method. [Copyright &y& Elsevier]

Abstract: This paper presents a high-accuracy method for fine registration of two partially overlapping point clouds that have been coarsely registered. The proposed algorithm, which is named dual interpolating point-to-surface method, is principally a modified variant of point-to-surface Iterative Closest Point (ICP) algorithm. The original correspondences are established by adopting a dual surface fitting approach using B-spline interpolation. A novel auxiliary pair constraint based on the surface fitting approach, together with surface curvature information, is employed to remove unreliable point matches. The combined constraint directly utilizes global rigid motion consistency in conjunction with local geometric invariant to reject false correspondences precisely and efficiently. The experimental results involving a number of realistic point clouds demonstrate that the new method can obtain accurate and robust fine registration for pairwise 3D point clouds. This method addresses highest accuracy alignment with less focus on recovery from poor coarse registrations. [Copyright &y& Elsevier]

Incident Photosynthetically Active Radiation (PAR) is a critical parameter for modelling ecosystem productivity. An algorithm for estimating instantaneous PAR from Moderate Resolution Imaging Spectroradiometer (MODIS) data was developed earlier; however, daily-integrated PAR is more meaningful than instantaneous PAR in many cases because many land surface models require a daily or coarser temporal resolution. This paper compares two different algorithms (adjusted sinusoidal interpolation and look-up table) for estimating daily-integrated PAR from instantaneous PAR values. Statistical analysis of the validation results indicates that the look-up table method more accurately estimates daily-integrated PAR than the use of adjusted sinusoidal interpolation. We also investigated how window size, daytime length and the number of overpass counts per day affect bias and the relative error of estimation. Validation using field measurements, and comparison with the Geostationary Operational Environmental Satellites PAR product, demonstrates that data collected by MODIS can be used to provide reliable estimates of daily-integrated PAR. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the application of Fresnel based numerical algorithms for the reconstruction of Gabor in-line holograms. We focus on the two most widely used Fresnel approximation algorithms, the direct method and the angular spectrum method. Both algorithms involve calculating a Fresnel integral, but they accomplish it in fundamentally different ways. The algorithms perform differently for different physical parameters such as distance, CCD pixel size, and so on. We investigate the constraints for the algorithms when applied to in-line Gabor digital holographic microscopy. We show why the algorithms fail in some instances and how to alter them in order to obtain useful images of the microscopic specimen. We verify the altered algorithms using an optically captured digital hologram. [Copyright &y& Elsevier]

Abstract: The simplified M-1D algorithm (M stands for modified) for the calculation of horizontal distribution of reflected brightness coefficient in 2D regions with large homogeneous pixels is presented. This algorithm is based upon modified 3⁎ N−1 1D-transport equations (where N is the number of large pixels) instead of one 2D-transport equation, usually used in such problems. The method does not rely on empiric assumptions on both optical properties of atmosphere or diffuse radiation intensity. Numerical results demonstrating the accuracy of the presented algorithm for simulating brightening and shadowing effects in a vicinity of the jump of optical properties given. The accuracy of the M-1D approximation strongly depends on the geometry and illumination conditions. However, it remains below 15% and can reach 1% for all cases studied and is strongly higher than the accuracy of usually employed independent pixel approximation. Time reduction via replacing 2D problem via modified 1D problem is about 17 times for all cases considered in this paper. [Copyright &y& Elsevier]

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while offering a numerical advantage in the sense of preconditioning. Next, we investigate weighted frames, in particular their relation to controlled frames. We consider the special case of semi-normalized weights, where the concepts of weighted frames and standard frames are interchangeable. We also make the connection with frame multipliers. Finally, we analyze weighted frames numerically. First, we investigate three possibilities for finding weights in order to tighten a given frame, i.e. decrease the frame bound ratio. Then, we examine Gabor frames and how well the canonical dual of a weighted frame is approximated by the inversely weighted dual frame. [ABSTRACT FROM AUTHOR]

Abstract: The Buchberger–Möller algorithm is a well-known efficient tool for computing the vanishing ideal of a finite set of points. If the coordinates of the points are (imprecise) measured data, the resulting Gröbner basis is numerically unstable. In this paper we introduce a numerically stable Approximate Vanishing Ideal (AVI) Algorithm which computes a set of polynomials that almost vanish at the given points and almost form a border basis. Moreover, we provide a modification of this algorithm which produces a Macaulay basis of an approximate vanishing ideal. We also generalize the Border Basis Algorithm ([Kehrein, A., Kreuzer, M., 2006. Computing border bases. J. Pure Appl. Algebra 205, 279–295]) to the approximate setting and study the approximate membership problem for zero-dimensional polynomial ideals. The algorithms are then applied to actual industrial problems. [Copyright &y& Elsevier]

Abstract: This paper presents a simple procedure for obtaining a numerical approximation to the consistent tangent matrix, together with a straightforward implicit (Euler backward) integration algorithm. The combined algorithm is used to incorporate four models into the commercial finite element package ABAQUS/Standard; illustrating how it can be used to rapidly implement material models within finite element analysis. The models have been chosen, not only because they help to illuminate the structure of the algorithm, but also because they illustrate its wide ranging applicability and permit the procedure to be tested against analytical results and an existing, well established, model. [Copyright &y& Elsevier]

Abstract  This paper presents an algorithm for the numerical approximation of spectral projectors onto the invariant subspaces corresponding to the eigenvalues inside, on, and outside the unit circle of a symplectic matrix. The algorithm constructs iteratively three matrix sequences from which the projectors are obtained. The convergence depends essentially on the gap between the unit circle and the eigenvalues inside it. A larger gap leads to faster convergence. Theoretical and algorithmic aspects of the algorithm are developed. Numerical results are reported. [ABSTRACT FROM AUTHOR]

In this paper we develop new methods for computing k-dimensional invariant manifolds of delayed systems for k ≥ 2. Our current implementation is built for k = 2 only, but the numerical and algorithmic challenges encountered in this case will be also present for any k > 1. For small delays, we consider methods for approximating delay differential equations (DDEs) with ordinary differential equations (ODEs). Once these approximations are made, any existing method for computing invariant manifolds of ODEs can then be used directly. We derive bounds on errors incurred by the most natural of these approximations. For large delays, we extend to DDEs the method originally introduced by Krauskopf and Osinga [Chaos, 9 (1999), pp. 768-774] for invariant manifolds of ODEs. We test the convergence of the resulting algorithms numerically and further illustrate our approach by computing two-dimensional unstable manifolds of equilibria in the context of phase-conjugate feedback lasers. [ABSTRACT FROM AUTHOR]

This paper shows how to compute O(√log n)-approximations to the Sparsest Cut and Balanced Separator problems in Õ(n²) time, thus improving upon the recent algorithm of Arora, Rao, and Vazirani [Proceedings of the 36th Annual ACM Symposium on Theory of Computing, 2004, pp. 222-231]. Their algorithm uses semidefinite programming and requires Õ (n9.5) time. Our algorithm relies on efficiently finding expander flows in the graph and does not solve semidefinite programs. The existence of expander flows was also established by Arora, Rao, and Vazirani. [ABSTRACT FROM AUTHOR]

This paper considers the problem of computing the real convex hull of a finite set of n-dimensional integer vectors. The starting point is a finite-automaton representation of the initial set of vectors. The proposed method consists in computing a sequence of automata representing approximations of the convex hull and using extrapolation techniques to compute the limit of this sequence. The convex hull can then be directly computed from this limit in the form of an automaton-based representation of the corresponding set of real vectors. The technique is quite general and has been implemented. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of boundary value problems in the reproducing kernel space. The analytical solution and approximate solution are represented in terms of series. For any initial function , we prove , , . Two numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective. [Copyright &y& Elsevier]

In this paper, we study the quadratic model updating problems by using symmetric low-rank correcting, which incorporates the measured model data into the analytical quadratic model to produce an adjusted model that matches the experimental model data, and minimizes the distance between the analytical and updated models. We give a necessary and sufficient condition on the existence of solutions to the symmetric low-rank correcting problems under some mild conditions, and propose two algorithms for finding approximate solutions to the corresponding optimization problems. The good performance of the two algorithms is illustrated by numerical examples. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In Part II of this paper we first refine the analysis of error-free vector transformations presented in Part I. Based on that we present an algorithm for calculating the rounded-to-nearest result of s := Σ pi for a given vector of floating-point numbers pi, as well as algorithms for directed rounding. A special algorithm for computing the sign of s is given, also working for huge dimensions. Assume a floating-point working precision with relative rounding error unit eps. We define and investigate a K-fold faithful rounding of a real number r. Basically the result is stored in a vector Resν of K nonoverlapping floating-point numbers such that Σ Resν approximates r with relative accuracy epsK, and replacing ResK by its floating-point neighbors in Σ Resν forms a lower and upper bound for r. For a given vector of floating-point numbers with exact sum s, we present an algorithm for calculating a K-fold faithful rounding of s using solely the working precision. Furthermore, an algorithm for calculating a faithfully rounded result of the sum of a vector of huge dimension is presented. Our algorithms are fast in terms of measured computing time because they allow good instruction-level parallelism, they neither require special operations such as access to mantissa or exponent, they contain no branch in the inner loop, nor do they require some extra precision. The only operations used are standard floating-point addition, subtraction, and multiplication in one working precision, for example, double precision. Certain constants used in the algorithms are proved to be optimal. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider a conic trust-region method for unconstrained optimization problems and analyze its convergence properties. We propose a convenient curvilinear search method to approximately solve the arising conic trust-region subproblem. Note that this approximate method preserves the strong convergence properties of the exact solution methods and is easy to implement. Both the linear and superlinear convergence of the method are established under commonly used conditions. Numerical experiments are conducted to show the efficiency of the new method. [Copyright &y& Elsevier]

This paper presents a new method for the numerical solution of nonlinear multiobjective optimization problems with an arbitrary partial ordering in the objective space induced by a closed pointed convex cone. This algorithm is based on the well-known scalarization approach by Pascoletti and Serafini and adaptively controls the scalarization parameters using new sensitivity results. The computed image points give a nearly equidistant approximation of the whole Pareto surface. The effectiveness of this new method is demonstrated with various test problems and an applied problem from medicine. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to construction interpolatory multiscaling functions with a general dilation factor . We first show two-scale matrix symbol associated with interpolatory multiscaling functions is reduced to a special form. Also, a characterization on approximation order for the multiscaling functions is described in terms of elements of this special two-scale matrix symbol. Then, an algorithm is provided for constructing compactly supported interpolating multiscaling functions with dilation factor and higher approximation order. Finally, the associated several families examples with one-parameter or two-parameters are explicitly presented. The optimal parameter values which make multiscaling functions provide the highest regularity are also computed. [Copyright &y& Elsevier]

Stochastic approximation problem is to find some root or extremum of a nonlinear function for which only noisy measurements of the function are available. The classical algorithm for stochastic approximation problem is the Robbins-Monro (RM) algorithm, which uses the noisy evaluation of the negative gradient direction as the iterative direction. In order to accelerate the RM algorithm, this paper gives a frame algorithm using adaptive iterative directions. At each iteration, the new algorithm goes towards either the noisy evaluation of the negative gradient direction or some other directions under some switch criterions. Two feasible choices of the criterions are proposed and two corresponding flame algorithms are formed. Different choices of the directions under the same given switch criterion in the flame can also form different algorithms. We also proposed the simultanous perturbation difference forms for the two flame algorithms. The almost surely convergence of the new algorithms are all established. The numerical experiments show that the new algorithms are promising. [ABSTRACT FROM AUTHOR]

Abstract: Regularized classifiers (a leading example is support vector machine) are known to be a kind of kernel-based classification methods generated from Tikhonov regularization schemes, and the polynomial kernels are the original and also probably the most important kernels used in them. In this paper, we provide an error analysis for the regularized classifiers using multivariate polynomial kernels. We introduce Bernstein–Durrmeyer polynomials, whose reproducing kernel Hilbert space norms and approximation properties in space play a key role in the analysis of regularization error. We also introduce the standard estimation of sample error, and derive explicit learning rates for these algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the algorithm in Xue and Cheng [L. Xue, X.L. Cheng, An algorithm for solving the obstacle problems, Comput. Math. Appl. 48 (2004) 1651–1657] for solving the double obstacle problem. We try to find the approximated region of the contact in the double obstacle problem with less computation time by iteration. Numerical example is given for the double obstacle problem for the elastic–plastic torsion problem to support the algorithm. [Copyright &y& Elsevier]

The maximum-likelihood detection (MLD) algorithm is the optimal detection scheme for vertical Bell Laboratories layered space-time (V-BLAST) systems. However, it is generally infeasible to implement the MLD algorithm in practical systems because of its high computational complexity. In this paper, we used two parallel interference cancellation techniques, including precancellation and postcancellation, to simplify the MLD algorithm into a class of computationally efficient suboptimal detection algorithms, herein called the generalized parallel interference cancellation (GPIC) algorithm. Numerical analysis shows that the GPIC algorithm can approximately achieve the MLD performance with considerably low and stable computational complexity. Furthermore, it can be significantly accelerated via parallel processing methods. With near-optimal performance, low and stable complexity, and high running speed, the GPIC algorithm is very suitable for real-time communication systems. [ABSTRACT FROM AUTHOR]

This paper presents a multidimensional extension of the Schur-Cohn algorithm for testing BIBO stability in N variables. This new method only needs a unique condition to be checked, as an alternative to the set of N conditions of the well-known Huang-Jury-Anderson stability test. The proposed algorithm is based on a generalization of the Schur coefficients recently obtained by the authors. In the two-variable case a simplification to the Sturm algorithm is presented, which can also be used in the case of a polynomial with complex coefficients. This approach is illustrated on several numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, a motion-compensated de-interlacing algorithm using the Markov random field (MRF) model is proposed. The de-interlacing problem is formulated as a maximum a posteriori (MAP) MRF problem. The MAP solution is the one that minimizes an energy function, which imposes discontinuity-adaptive smoothness (DAS) spatial constraint on the de-interlaced frame. The edge direction information, which is used to formulate the DAS constraint, is implicitly indicated by weight vectors (weights for 16 digitized directions). Generally, large weights are assigned to along-edge directions and relatively small weights are assigned to across-edge directions. As a local statistical-based method, the proposed weighting method should be more robust than traditional edge-directed interpolation methods in deciding local edge directions. The proposed algorithm is implemented by an iterative optimization process, which guarantees convergence. However, a global optimal solution is not guaranteed due to computational complexity concern. Simulation results compare the proposed algorithm to other motion compensated de-interlacing algorithms. Significant improvements of de-interlaced edges are observed. [ABSTRACT FROM AUTHOR]

The Digital Elevation Model that has been derived from the February 2000 Shuttle Radar Topography Mission (SRTM) has been one of the most important publicly available new spatial data sets in recent years. However, the 'finished' grade version of the data (also referred to as Version 2) still contains data voids (some 836,000 km2) - and other anomalies - that prevent immediate use in many applications. These voids can be filled using a range of interpolation algorithms in conjunction with other sources of elevation data, but there is little guidance on the most appropriate void-filling method. This paper describes: (i) a method to fill voids using a variety of interpolators, (ii) a method to determine the most appropriate void-filling algorithms using a classification of the voids based on their size and a typology of their surrounding terrain; and (iii) the classification of the most appropriate algorithm for each of the 3,339,913 voids in the SRTM data. Based on a sample of 1304 artificial but realistic voids across six terrain types and eight void size classes, we found that the choice of void-filling algorithm is dependent on both the size and terrain type of the void. Contrary to some previous findings, the best methods can be generalised as: kriging or inverse distance weighting interpolation for small and medium size voids in relatively flat low-lying areas; spline interpolation for small and medium-sized voids in high-altitude and dissected terrain; triangular irregular network or inverse distance weighting interpolation for large voids in very flat areas, and an advanced spline method (ANUDEM) for large voids in other terrains. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an efficient numerical algorithm for approximate solutions of a fractional population growth model in a closed system. The time-fractional derivative is considered in the Caputo sense. The algorithm is based on Adomian’s decomposition approach and the solutions are calculated in the form of a convergent series with easily computable components. Then the Padé approximants are effectively used in the analysis to capture the essential behavior of the population u(t) of identical individuals. [Copyright &y& Elsevier]