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In this paper, we propose a generalized Laguerre spectral method for Fisher's-type equation with inhomogeneous boundary conditions on a semi-infinite interval. By reformulating the equation with suitable functional transform, it is shown that the generalized Laguerre approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the generalized Laguerre approximations to the transformed equation is developed and implemented. Numerical results show the efficiency of this approach and coincide well with theoretical analysis. [ABSTRACT FROM PUBLISHER]

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented. [ABSTRACT FROM AUTHOR]

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]

Three-dimensional (3D) linear and circular interpolations are a basic element in the machining of complex shapes. Because of the lack of accurate and efficient algorithms for the generation of 3D lines and circles, a full realization for the available machine tool resolution is difficult. This paper presents new algorithms for 3D linear and circular interpolation in the reference pulse technique. In 3D space, the line or circle cannot be represented as a general implicit equation. The natural way to represent a line or circle is as the intersection of two surfaces. Based on these facts, interpolation algorithms were designed to follow intersection curves in searching for a minimum path error strategy, and a real-time 3D linear and circular interpolator was developed in software using a PC. The software implementations in a PC and the hardware implementation on a retrofitted milling machine have shown promising results in interpolation error and speed performance. It is expected that this can be applied to the computerized numerical control systems for the machining of 3D lines, circles and some other complex shapes. [ABSTRACT FROM AUTHOR]

In this paper, a novel hybrid method based on two approaches, evolutionary algorithms and an iterative scheme, for obtaining the approximate solution of optimal control governed by nonlinear Fredholm integral equations is presented. By converting the problem to a discretized form, it is considered as a quasi-assignment problem and then an iterative method is applied to find an approximate solution for the discretized form of the integral equation. An analysis for convergence of the proposed iterative method and its implementation for numerical examples are also given. [ABSTRACT FROM AUTHOR]

In this paper, we consider a rational algorithm for modification of a positive measure by quadratic factor, , where it is allowed z to be in supp(d σ). Also, we present an application of modified algorithm to the measures and , where T 2(t)=t 2−½ is the second degree monic Chebyshev polynomial of the first kind and , , is the Chebyshev measure of the second kind. Also, we present an application to the constrained L 2-polynomial approximation. [ABSTRACT FROM AUTHOR]

We propose a quasi-Newton line-search method that uses negative curvature directions for solving unconstrained optimization problems. In this method, the symmetric rank-one (SR1) rule is used to update the Hessian approximation. The SR1 update rule is known to have a good numerical performance; however, it does not guarantee positive definiteness of the updated matrix. We first discuss the details of the proposed algorithm and then concentrate on its practical behaviour. Our extensive computational study shows the potential of the proposed method from different angles, such as its performance compared with some other existing packages, the profile of its computations, and its large-scale adaptation. We then conclude the paper with the convergence analysis of the proposed method. [ABSTRACT FROM AUTHOR]

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]

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]

This paper deals with the existence and necessary optimality conditions for an optimal control problem governed by a phase-field transition system. The one-point boundary (time variable) state condition is considered. A numerical algorithm of gradient type and numerical implementation are reported, too. [ABSTRACT FROM AUTHOR]

We present a first-order approach for solving semidefinite programs. The goal of this approach is to compute a solution of the semidefinite program (SDP) up to a high accuracy in spite of using only partial second-order information. We propose a hybrid approach that uses an accelerated projection method to generate an approximate solution and then switches to the quasiminimal residual algorithm (QMR) algorithm applied to a symmetrized version of the Alizadeh-Haeberly-Overton (AHO) system to improve this approximation. Some numerical experiments based on a number of random test examples illustrate the potential of this approach. [ABSTRACT FROM PUBLISHER]

We present a new method for computing zeros of polynomial systems using the algebraic solver and the QR-method. It is based on the theory of algebraic solvers. The unstable calculation of the determinant of the large matrix is replaced by a stable technique using the QR-method. Algorithms and numerical results are presented. [ABSTRACT FROM AUTHOR]

This study aimed at assessing the applicability of a robust method to determine and correct lens distortion before using the direct linear transformation (DLT) algorithm in three-dimensional motion analysis. The known length of a rigid bar was reconstructed under different conditions of working volume (interpolation or extrapolation), number of cameras (2 or 4), position of the cameras (wide or narrow angle between optical axes), camera focal distance (4 or 8 mm) and number of control points (CPs; 8, 12, 18 or 162), through four different camera set-ups. The accuracy (percent root mean square error) of Set-up 2 (non-extrapolated working volume; two cameras; 4 mm focal distance; narrow optical axes angle) decreased with less CPs (162: 0.73%; 8: 2.78%). Set-up 1 (non-extrapolated working volume; two cameras; 8 mm focal distance; wide optical axes angle), Set-up 3 (Set-ups 1 and 2 used simultaneously) and Set-up 4 (extrapolated working volume; two cameras; 4 mm focal distance; wide optical axes angle) showed minor differences in accuracy across groups of CPs, with maximum values of 0.84%, 1.20% and 1.71%, respectively. Random errors were the main source of decreased accuracy of Set-ups 2 and 4.The proposed procedure enables accurate results with no modification in the DLT-based analysis system, even with smaller calibration frames, less CPs and wide field-of-view cameras. [ABSTRACT FROM AUTHOR]

In our terminology 'globally convergent numerical method' means a numerical method, whose convergence to a good approximation for the correct solution is independent of the initial approximation. A new numerical imaging algorithm has been proposed to solve a coefficient inverse problem for an elliptic equation with the data generated by computer simulation. A rigorous convergence analysis shows that this method converges globally. A heuristic approach for approximating the 'new tail-function', which is a crucial part (assuming the smallness of the tail-function) of our problem, has been utilized and verified in numerical experiments, so as the global convergence. Applications to both optical and thermal tomography are discussed. Numerical experiments in the 2D thermal property reconstruction are presented. [ABSTRACT FROM AUTHOR]

This article proposes and analyses a novel heuristic rule for choosing regularization parameters in Tikhonov regularization for inverse problems. The existence of solutions to the regularization parameter equation is shown, and a variational characterization of the inverse solution is provided. Some a posteriori error estimates of the approximate solutions to the inverse problem are also established. An iterative algorithm is suggested for the efficient numerical realization of the new choice rule, which is shown to have a practically desirable monotone convergence. Numerical experiments for both mildly and severely ill-posed benchmark inverse problems with various regularizing functionals of Tikhonov type, e.g. L2-L2 with constraints, L2-ℓ1 and L1-TV, are presented to demonstrate its effectiveness, and compared with the quasi-optimality criterion. [ABSTRACT FROM AUTHOR]

An optimal control problem governed by the first bi-harmonic equation with the integral constraint for the state and its spectral approximations based on a mixed formulation are investigated. The optimality conditions of the exact and the discrete optimal control systems are derived. The a priori error estimates of high order spectral accuracy are obtained. Furthermore, a simple and efficient iterative algorithm is proposed to solve mixed discrete system. Some numerical examples are performed to verify the theoretical results. [ABSTRACT FROM AUTHOR]

A semilinear parabolic problem with a nonlocal Dirichlet boundary condition is studied. This article presents a new and very easy implementable numerical algorithm for computations. This is based on a suitable linearization in time. The derived algorithm is implicit and it does not need any iteration process to get a solution with the nonlocal boundary condition. The stability analysis has been performed and the convergence of approximations towards a solution of the continuous problem is shown. The uniqueness of a solution is proved. Error estimates for the time discretization are derived. [ABSTRACT FROM AUTHOR]

This study is on valuing Asian strike options and presents efficient and accurate quadratic approximation methods that work extremely well, both with regard to the volatility of a wide range of underlying assets, and longer average time windows. We demonstrate that most of the well-known quadratic approximation methods used in the literature for pricing Asian strike options are special cases of our model, with the numerical results demonstrating that our method significantly outperforms the other quadratic approximation methods examined here. Using our method for the calculation of hundreds of Asian strike options, the pricing errors (in terms of the root mean square errors) are reasonably small. Compared with the Monte Carlo benchmark method, our method is shown to be rapid and accurate. We further extend our method to the valuing of quanto forward-starting Asian strike options, with the pricing accuracy of these options being largely the same as the pricing of plain vanilla Asian strike options. [ABSTRACT FROM AUTHOR]

A novel center of charge method (CCM) is introduced to solve multi-conductor capacitance extraction problems. It combines the features of Appel's algorithm and the fast multipole algorithm (FMA). the second order CCM as well as the first order CCM are derived to approximate the far field. The symmetry in the solution can be preserved and the charge distribution can be improved through the second order approximation. The relations between CCM and FMA are studied. Numerical examples demonstrate that CCM uses less CPU time, needs less memory and has very good accuracy compared to MoM and FMA. [ABSTRACT FROM AUTHOR]