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Particle-based methods based on material models using spheres can provide good approximations for many physical phenomena at both the micro and macroscales. The point of departure for the simulations, in general, is a dense arrangement of spherical particles (sphere pack) inside a given container. For generic domains, the generation of a sphere pack may be complex and time-consuming, especially if the pack must comply with a prescribed sphere size distribution and the stability requirements of the simulation. The primary goal of this paper is to present an efficient algorithm that is capable of producing packs with millions of spheres following a statistical sphere size distribution inside complex arbitrary domains. This algorithm uses a new strategy to ensure that the sphere size distribution is preserved even when large particles are rejected in the growing process. The paper also presents numerical results that enable an evaluation of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Variable selection methods have been widely used for system identification. However, there is still a major challenge in producing parsimonious models with optimal model structures as popular variable selection methods often produce suboptimal model with redundant model terms. In the paper, stability orthogonal regression (SOR) is proposed to build a more compact model with fewer or no redundant model terms. The main idea of SOR is that multiple intermediate models are produced by orthogonal forward regression (OFR) using sub-sampling technique and then the final model is a combination of these intermediate model terms but does not include infrequently selected terms. The effectiveness of the proposed methods is analyzed in theory and also demonstrated using two numerical examples in comparison with some popular algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we significantly extend the applicability of state-of-the-art ELDP (equations for linearizing discrete product terms) method by providing a new linearization to handle more complicated non-linear terms involving both of discrete and bounded continuous variables. A general class of “representable programming problems” is formally proposed for a much wider range of engineering applications. Moreover, by exploiting the logarithmic feature embedded in the discrete structure, we present an enhanced linear reformulation model which requires half an order fewer equations than the original ELDP. Computational experiments on various engineering design problems support the superior computational efficiency of the proposed linearization reformulation in solving engineering optimization problems with discrete and bounded continuous variables. [ABSTRACT FROM AUTHOR]

Abstract: The linear complementarity problem is to find a vector in satisfying , ,, where and are given. In this paper, we use the fact that solving is equivalent to solving the nonlinear equation where is a function from into itself defined by . We build a sequence of smooth functions which is uniformly convergent to the function . We show that, an approximation of the solution of the (when it exists) is obtained by solving for a parameter large enough. Then we give a globally convergent hybrid algorithm which is based on vector divisions and the secant method for solving . We close our paper with some numerical simulations to illustrate our theoretical results, and to show that this method can solve efficiently large-scale linear complementarity problems. [Copyright &y& Elsevier]

Abstract: Morphing is an interpolation technique that changes one form into another through a seamless transition, producing, in the process, an infinite number of ‘intermediate’ forms between the original and the target. This paper examines the possibility of using the morphing technique for generating a large number of hull forms rapidly based on a number of target forms, existing or newly generated. The paper discusses the technique developed for applying morphing technique to hull form definition. The algorithm first projects the vertices of the original and target 3D surfaces onto 2D planes. After ‘regularising’ the vertices on 2D, they are projected back on the 3D surfaces. The corresponding vertices of the two surfaces are then used for interpolation. It has been found that the interpolated hull forms can be generated almost instantaneously, allowing the whole algorithm to be embedded in an optimisation program. [Copyright &y& Elsevier]

Abstract: The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing quasi-Newton method for the solution of the nonlinear complementarity problems by constructing a new smoothing approximation function. Global and local superlinear convergence results of the proposed algorithm are established under suitable conditions. Some numerical results are reported in the paper. [Copyright &y& Elsevier]

This paper presents an approach to the interpolation of angular feedrate for bi-parameter curve paths in multi-axis machining. A bi-parameter curve is the intersection of a parametric surface and an implicit surface. A tool path is identified by a position curve and an orientation curve, both of which are generated based on the bi-parameter curve. The angular feedrate interpolator calculates the tool position and orientation at each sampling cycle according to the specified angular feedrates and the given tool path. The paper analytically relates the angular arc-length derivatives to the time derivatives of the parameters along the path making use of both angular feedrates and angular feed acceleration. The results are then used to interpolate the parameters of the bi-parameter curve leading to an accurate calculation of the position and orientation of the cutting tool. A general parametric surface has been used to verify the effectiveness of the algorithm. The bi-parameter curves of the surface have been computed for arbitrarily selected intersecting cylinders. [Copyright &y& Elsevier]

In this paper, a new composite rough set model is proposed to process incomplete composite information with criteria and regular attributes. Following that, some strategies for incrementally updating approximations of composite rough sets when adding or removing some objects are discussed and the corresponding incremental algorithms are designed. Several numerical examples illustrate the feasibilities of the composite rough set model and the incremental strategies, respectively. Experimental evaluation shows that the incremental algorithms can effectively reduce the running time than their counterparts. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a reweighted nuclear norm minimization algorithm based on the weighted fixed point method (RNNM–WFP algorithm) to recover a low rank matrix, which iteratively solves an unconstrained minimization problem introduced as a nonconvex smooth approximation of the low rank matrix minimization problem. We prove that any accumulation point of the sequence generated by the RNNM–WFP algorithm is a stationary point of the minimization problem. Numerical experiments on randomly generated matrix completion problems indicate that the proposed algorithm has better recoverability compared to existing iteratively reweighted algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, a practical bivariate Newton–Thiele type matrix Padé approximation is introduced by using the generalized inverse of a matrix. The approximants are expressed in the form of Newton expansion and branched continued fractions, which can be computed by an efficient recursive algorithm. Some algebraic properties are also discussed and the application in state-space realization of the 2-D filters is given in the end. [Copyright &y& Elsevier]

Abstract: Standard model order reduction techniques attempt to build reduced order models of large scale systems with similar input–output behavior over a wide range of input frequencies as the full system models. The method known as the dominant pole algorithm has previously been successfully used in combination with model order reduction techniques to approximate standard linear time-invariant dynamical systems and second order dynamical systems as well as nonlinear time-delay systems. In this paper, we show that the dominant pole algorithm can be adapted for parametric systems where these parameters usually have physical meaning. There are two approaches for finding dominant poles. These algorithms are illustrated by the second order numerical examples. [Copyright &y& Elsevier]

Abstract: A simple algorithm for computing an approximate parameterization of real space algebraic curves using their graphs of critical points is designed and studied in this paper. The first step is determining a suitable space graph which contains all critical points of a real algebraic space curve implicitly defined as the complete intersection of two surfaces. The construction of this graph is based on one projection of in a general position onto an -plane and on an intentional choice of vertices. The second part of the designed method is a computation of a spline curve which replaces the edges of the constructed graph by segments of a chosen free-form curve. This step is formulated as an optimization problem when the objective function approximates the integral of the squared Euclidean distance of the constructed approximate curve to the intersection curve. The presented method, based on combining symbolic and numerical steps to the approximation problem, provides approximate parameterizations of space algebraic curves from a small number of approximating arcs. It may serve as a first step to several problems originating in technical practice where approximation curve parameterizations are needed. [Copyright &y& Elsevier]

Abstract: In this paper we present a novel fast mesh parameterization algorithm based on subdivision scheme. First, an algorithm of approximating a given triangular mesh by the 4-point interpolatory subdivision is proposed, then a mesh parameterization method is developed based on the subdivision surface approximation algorithm. The novel mesh parameterization method is a generalization of the chordal parameterization to surface case, and it is more computationally efficient than previous methods because it obviates any computation of linear system of equations. Some numerical experiments show the efficiency of the novel algorithm. [Copyright &y& Elsevier]

Abstract: A deflated restarting Krylov subspace method for approximating a function of a matrix times a vector is proposed. In contrast to other Krylov subspace methods, the performance of the method in this paper is better. We further show that the deflating algorithm inherits the superlinear convergence property of its unrestarted counterpart for the entire function and present the results of numerical experiments. [Copyright &y& Elsevier]

Abstract: This paper addresses pattern classification in dynamical systems, where the underlying algorithms are formulated in the symbolic domain and the patterns are constructed from symbol strings as probabilistic finite state automata (PFSA) with (possibly) diverse algebraic structures. A combination of Dirichlet and multinomial distributions is used to model the uncertainties due to the (finite-length) string approximation of symbol sequences in both training and testing phases of pattern classification. The classifier algorithm follows the structure of a Bayes model and has been validated on a simulation test bed. The results of numerical simulation are presented for several examples. [Copyright &y& Elsevier]

Abstract: In this paper, a new three-level compact alternating direction implicit (ADI) difference scheme is derived for solving a kind of nonlinear wave equations. Basing on a fourth-order approximation to the exact solution at the first time level, it is shown by the energy method that the numerical solution is conditionally convergent with an order of in - and -norms. A new Richardson extrapolation formula based on three time-grid parameters is given to get numerical solution of fourth-order accuracy in both time and space. The performance of the new algorithm is illustrated by numerical experiments. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a compact alternating direction implicit (ADI) scheme for solving the two-dimensional parabolic equation. The maximum norm convergence is proven, and the convergence rate is second-order in time and fourth-order in space. We develop a Richardson extrapolation algorithm to increase the accuracy to sixth-order both in time and space. Numerical experiments show the effectiveness of the method. [Copyright &y& Elsevier]

Abstract: This paper examines the design of liner ship route schedules that can hedge against the uncertainties in port operations, which include the uncertain wait time due to port congestion and uncertain container handling time. The designed schedule is robust in that uncertainties in port operations and schedule recovery by fast steaming are captured endogenously. This problem is formulated as a mixed-integer nonlinear stochastic programming model. A solution algorithm which incorporates a sample average approximation method, linearization techniques, and a decomposition scheme, is proposed. Extensive numerical experiments demonstrate that the algorithm obtains near-optimal solutions with the stochastic optimality gap less 1.5% within reasonable time. [Copyright &y& Elsevier]

Abstract: To solve a general class of elliptic operator equations, Cohen et al. (2001) [2] designed two adaptive wavelet algorithms that yield an approximate solution with error . In this paper, we modify the error analysis for the second algorithm and optimize the upper bound. Numerical experiments demonstrate that our approximation has some advantages compared to that of the reference. [Copyright &y& Elsevier]

Abstract: In this paper, we present a numerical approach for solving the system of multi-pantograph equations with mixed conditions. This system is usually difficult to solve analytically. By expanding the approximate solutions by means of the Bessel functions of first kind with unknown coefficients, the proposed approach consists of reducing the problem to a linear algebraic equation system. The unknown coefficients of the Bessel functions of first kind are computed using the matrix operations of derivatives together with the collocation method. An error estimation is given. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples. All of the numerical computations have been performed on a computer with the aid of a program written in Matlab. [Copyright &y& Elsevier]

Abstract: This paper considers bi-criteria scheduling on a single parallel-batch machine to minimizing two regular scheduling criteria that are non-decreasing in the job completion times. For minimizing the total weighted completion time and the makespan simultaneously, we prove that the problem is NP-hard in the ordinary sense and possesses a fully polynomial-time approximation scheme. For minimizing the weighted total number of tardy jobs and the makespan simultaneously, we provide a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme. Furthermore, we identify that all Pareto-optimal solutions for and can be found in pseudo-polynomial time, respectively. [Copyright &y& Elsevier]

Abstract: Weighted essentially non-oscillatory (WENO) schemes have been mainly used for solving hyperbolic partial differential equations (PDEs). Such schemes are capable of high order approximation in smooth regions and non-oscillatory sharp resolution of discontinuities. The base of the WENO schemes is a non-oscillatory WENO approximation procedure, which is not necessarily related to PDEs. The typical WENO procedures are WENO interpolation and WENO reconstruction. The WENO algorithm has gained much popularity but the basic idea of approximation did not change much over the years. In this paper, we first briefly review the idea of WENO interpolation and propose a modification of the basic algorithm. New approximation should improve basic characteristics of the approximation and provide a more flexible framework for future applications. New WENO procedure involves a binary tree weighted construction that is based on key ideas of WENO algorithm and we refer to it as the binary weighted essentially non-oscillatory (BWENO) approximation. New algorithm comes in a rational and a polynomial version. Furthermore, we describe the WENO reconstruction procedure, which is usually involved in the numerical schemes for hyperbolic PDEs, and propose the new reconstruction procedure based on the described BWENO interpolation. The obtained numerical results show that the newly proposed procedures perform very well on the considered test examples. [Copyright &y& Elsevier]

Abstract: The conventional multislice method (CMS), originally proposed by , is an important algorithm for image and electron diffraction calculations in transmission electron microscopy. Nevertheless, this method is based on the so-called high-energy approximation, which neglects the second differential term ∂2 φ(r)/∂z 2 to greatly simplify the calculation without severe loss of accuracy. In the current study, we show that for low-energy transmission electron microscopy (LE-TEM) (<100kV), the high-energy approximation error becomes large and the accurate multislice method, proposed by , can be used as an alternative method to obtain more accurate calculations. The accurate multislice method, called the revised real space method (RRS) in this paper, can be realized by treating the propagation and scattering as an entirety in real space. A detailed comparison of the numerical results of the RRS and CMS at different accelerating voltages, Debye–Waller factors, and beam tilts is performed. Results show that for image and diffraction simulations in LE-TEM, CMS is no longer sufficiently accurate and the RRS procedure can be used as an alternative method with reasonable computing time. [Copyright &y& Elsevier]

Abstract: Recently, graph-based spectral clustering algorithms have been developing rapidly, which are proposed as discrete combinatorial optimization problems and approximately solved by relaxing them into tractable eigenvalue decomposition problems. In this paper, we first review the current existing spectral clustering algorithms in a unified-framework way and give a straightforward explanation about spectral clustering. We also present a novel model for generalizing the unsupervised spectral clustering to semi-supervised spectral clustering. Under this model, prior information given by some instance-level constraints can be generalized to space-level constraints. We find that (undirected) graph built on the enlarged prior information is more meaningful, hence the boundaries of the clusters are more correct. Experimental results based on toy data, real-world data and image segmentation demonstrate the advantages of the proposed model. [Copyright &y& Elsevier]

Abstract: The problem of finding the least change adjustment to a stiffness matrix modeled by finite element method is considered in this paper. Desired stiffness matrix properties such as symmetry, sparsity, positive semidefiniteness, and satisfaction of the characteristic equation are imposed as side constraints of the constructed optimal matrix approximation for updating the stiffness matrix, which matches measured data better. The dual problems of the original constrained minimization are presented and solved by subgradient algorithms with different line search strategies. Some numerical results are included to illustrate the performance and application of the proposed methods. [Copyright &y& Elsevier]

Abstract: In this paper a modified gradient based algorithm for solving Sylvester equations is presented. Different from the gradient based method introduced by Ding and Chen and the relaxed gradient based algorithm proposed by Niu et al. , the information generated in the first half-iterative step is fully exploited and used to construct the approximate solution. Theoretical analysis shows that the new method converges under certain assumptions. Numerical results are given to verify the efficiency of the new method. [Copyright &y& Elsevier]

Abstract: In this paper, two iterative algorithms are proposed to solve the linear matrix equations . When the matrix equations are consistent, by the first algorithm, a solution can be obtained within finite iterative steps in the absence of roundoff-error for any initial value, furthermore, the minimum-norm solution can be got by choosing a special kind of initial matrix. Additionally, the unique optimal approximation solution to a given matrix can be derived by finding the minimum-norm solution of a new matrix equations . When the matrix equations are inconsistent, we present the second algorithm to find the least-squares solution with the minimum-norm. Finally, two numerical examples are tested by MATLAB, the results show that these iterative algorithms are efficient. [Copyright &y& Elsevier]

Abstract: This paper describes a numerical approximation to the solution of Volterra integral equations of the second kind. This algorithm combines trapezoidal and Simpson rules. We prove the convergence of the method. Numerical examples are provided to illustrate the accuracy of the method. [Copyright &y& Elsevier]

Abstract: In the present paper, we present block Arnoldi-based methods for the computation of low rank approximate solutions of large discrete-time algebraic Riccati equations (DARE). The proposed methods are projection methods onto block or extended block Krylov subspaces. We give new upper bounds for the norm of the error obtained by applying these block Arnoldi-based processes. We also introduce the Newton method combined with the block Arnoldi algorithm and present some numerical experiments with comparisons between these methods. [Copyright &y& Elsevier]

Abstract: The Jacobian-free Newton–Krylov (JFNK) method is a special kind of Newton–Krylov algorithm, in which the matrix-vector product is approximated by a finite difference scheme. Consequently, it is not necessary to form and store the Jacobian matrix. This can greatly improve the efficiency and enlarge the application area of the Newton–Krylov method. The finite difference scheme has a strong influence on the accuracy and robustness of the JFNK method. In this paper, several methods for approximating the Jacobian-vector product, including the finite difference scheme and the finite difference step size, are analyzed and compared. Numerical results are given to verify the effectiveness of different finite difference methods. [Copyright &y& Elsevier]

Abstract: Expensive optimization aims to find the global minimum of a given function within a very limited number of function evaluations. It has drawn much attention in recent years. The present expensive optimization algorithms focus their attention on metamodeling techniques, and call existing global optimization algorithms as subroutines. So it is difficult for them to keep a good balance between model approximation and global search due to their two-part property. To overcome this difficulty, we try to embed a metamodel mechanism into an efficient evolutionary algorithm, low dimensional simplex evolution (LDSE), in this paper. The proposed algorithm is referred to as the low dimensional simplex evolution extension (LDSEE). It is inherently parallel and self-contained. This renders it very easy to use. Numerical results show that our proposed algorithm is a competitive alternative for expensive optimization problems. [Copyright &y& Elsevier]

Abstract: In this paper, an algorithm for approximate calculation of the attainable sets of nonlinear control systems with integral constraint on controls is presented. A numerical example of the computer application of this algorithm is also given. [Copyright &y& Elsevier]

Abstract: In this paper we propose an iterative algorithm to solve large size linear inverse ill posed problems. The regularization problem is formulated as a constrained optimization problem. The dual Lagrangian problem is iteratively solved to compute an approximate solution. Before starting the iterations, the algorithm computes the necessary smoothing parameters and the error tolerances from the data. The numerical experiments performed on test problems show that the algorithm gives good results both in terms of precision and computational efficiency. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new symmetric rank-one (SR1) method for the solution of unconstrained optimization problems. The proposed method involves an algorithm in which the usual SR1 Hessian is updated a number of times in a way to be specified in some iterations, to improve the performance of the Hessian approximation. In particular, we discuss how to consider a criterion for indicating at each iteration whether it is necessary to employ extra updates. However it is well known that there are some theoretical difficulties when applying the SR1 update. Even for a current positive definite Hessian approximation, it is possible that the SR1 update may not be defined or the SR1 update may not preserve positive definiteness at some iterations. We then employ a restarting procedure that guarantees that updated matrices will be well-defined while preserving positive definiteness of updates. Numerical results support these theoretical considerations. They show that the implementation of the SR1 method using extra updating techniques improves the performance of the SR1 method substantially for a number of test problems from the literature. [Copyright &y& Elsevier]

Abstract: In this paper we introduce a new boundary condition that can be used when reconstructing an image from observed blurred and noisy data. Our approach uses information from the observed image to enforce boundary conditions that continue image features such as edges and texture across the boundary. Because of its similarity to methods used in texture synthesis, we call our approach synthetic boundary conditions. We provide an efficient algorithm for implementing the new boundary condition, and provide a linear algebraic framework for the approach that puts it in the context of more classical and well known image boundary conditions, including zero, periodic, reflective, and anti-reflective. Extensive numerical experiments show that our new synthetic boundary conditions provide a more accurate approximation of the true image scene outside the image boundary, and thus allow for better reconstructions of the unknown, true image scene. [Copyright &y& Elsevier]

Abstract: We introduce in this paper a new direction splitting algorithm for solving the incompressible Navier–Stokes equations. The main originality of the method consists of using the operator (I − ∂ xx )(I − ∂ yy )(I − ∂ zz ) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2×109 points. [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]

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]

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: 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]