Showing papers in "Journal of Computational and Applied Mathematics in 1988"

TL;DR: The preconditioned conjugate gradient method is used to solve the system of linear equations Ax = b, where A is a singular symmetric positive semi- definite matrix and the theory is applied to the discretized semi-definite Neumann problem.

TL;DR: An incomplete LQ factorization is proposed and some of its implementation details are described and a number of experiments are reported to compare these methods.

TL;DR: In this article, a symmetric singular value decomposition A=Q∑QT is presented for the complex square matrix A and an algorithm for the computation of this decomposition is presented.

TL;DR: It is shown that the four vector extrapolation methods, minimal polynomial extrapolation, reduced rank extrapolations, modified minimal Pooleian extrapolation and topological epsilon algorithm, when applied to linearly generated vector sequences, are Krylov subspace methods, and are equivalent to some well known conjugate gradient type methods.

TL;DR: In this paper, the authors established convergence of the method of tangent hyperbolas for solving nonlinear equations in Banach spaces as well as the existence and uniqueness of solution.

TL;DR: In this article, a FORTRAN program for the numerical solution of Abel-Volterra convolution equations of the second and first kind was given, using a fractional linear multistep method (BDF4) 1 2 and use Fast Fourier transform techniques to exploit the convolution structure.

TL;DR: In this paper, the convergence and stability results for the following vector extrapolation methods were presented: Minimal Polynomial Extrapolation (MPE), Reduced Rank Extrapolations (RSE), Modified MPE, and Topological Epsilon Algorithm (TEE).

TL;DR: The difference scheme via spline in tension for the problem: − ϵy″ + p (x)y = f(x), p(x)\s>0, y(0) = α 0, y (1) =α 1, is derived in this paper.

TL;DR: In this paper, a singularly perturbed linear parabolic initial-boundary value problem in one space variable was examined and various finite difference schemes were derived for this problem using a semidiscrete Petrov-Galerkin finite element method.

TL;DR: The aim of this paper is to review the properties of the various iteration methods for the numerical solution of very large, sparse linear systems of equations, in order to assist the user in making a deliberate selection.

TL;DR: In this article, a formula expressing the Chebyshev coefficients of the general order derivative of an infinitely differentiable function in terms of its Chebyhev coefficient is suggested.

TL;DR: In this article, a new approach for semi-infinite programming problems is presented, which belongs to the class of successive quadratic programming (SQP) methods with trust region technique.

TL;DR: Bounds are calculated for the average performance of the power method for the calculation of eigenvectors of symmetric and Hermitian matrices, thus an upper bound is found for theaverage complexity of Eigenvector calculation.

TL;DR: An algorithm for computing co-monotone and/or co-convex splines of degree m and deficiency m − k at the knots, which are interpolant or osculatory to a given set of data, is described.

TL;DR: It is shown that sparse direct solvers generalize naturally to methods based on high-order elements, and that directsolvers are adequate for two-dimensional problems, especially for multiple load vectors.

TL;DR: In this paper, De Montessus-De Ballore type convergence theorems for row sequences of vector-valued approximants to meromorphic vector functions have been established.

TL;DR: In this article, the authors constructed a spectral scheme for the periodic initial value problem for a system of equations of the complex Schrodinger field, interacting with the real Klein-Gordon field.

TL;DR: From the model problem analysis it follows that the overcorrection can substantially improve the reduction of smooth error components and change favourably the properties of the multilevel aggregation correction method.

TL;DR: In this article, a simple three-point formula is constructed for the evaluation of general oscillatory integrals and a rigorous derivation of the local error term is presented, and the implications to high frequency oscillations are discussed.

TL;DR: By the use of the proposed method, a fairly sharp estimate of the rounding error in the function evaluation is obtained, on the basis of which a computationally meaningful norm may be introduced in the space of residuals to afford a convergence criterion for an iterative method of solving the system of nonlinear equations.

TL;DR: In this article, a fourth-order cubic spline method for second-order nonlinear two-point boundary-value problems was proposed, which provides order h 4 uniformly convergent approximations over [ a, b ].

TL;DR: In this article, the authors derived simple estimates for the expected 2-norm of random matrices A with elements from a normal distribution with zero mean and standard deviation σ, and from a Poisson distribution with mean value λ.

TL;DR: In this paper, the authors presented two fast procedures for numerical solution of the discrete Riemann-Hilbert problem: a conjugate gradient method with computational cost O( N log N ) and a Toeplitz matrix method with O(N log 2 N ).

TL;DR: In this paper, a general dynamic finite horizon spatial price equilibrium model is presented, where inventorying is allowed at both supply and demand markets and backordering is also permitted for as many time periods as dictated by the competitive equilibrium.

TL;DR: The lattice structure of these matrix generators used in Monte-Carlo simulations is studied in order to assess stochastical properties of the generated pseudo-random vectors.

TL;DR: Two iterative methods are considered, Richardson's method and a general second order method for which only even numbered iterants are computed, called leapfrog method and grand-leap method.

TL;DR: An analysis of some of the tradeoffs involved in the design and efficient implementation of conjugate gradient-based algorithms for a multivector processor with a two-level memory hierarchy is presented and supplemented by experimental results obtained on an Alliant FX/8.

TL;DR: In this article, the iterated Galerkin method of I.H. Sloan was generalized to get similar results for the larger class of integro differential equations, and two approaches were investigated to obtain superconvergence in different norms.

TL;DR: Etude des differences reciproques multivariables pour les developpements en fractions continues de Thiele ramifiees as discussed by the authors, see Section 5.1.

TL;DR: The Partial Total Least Squares (PTLS) subroutine as mentioned in this paper solves the PTLS problem AX ≈ B by using a Partial Singular Value Decomposition (PSVD), thereby improving the computational efficiency of the classical TLS algorithm.