Journal ArticleDOI
An optimum iterative method for solving any linear system with a square matrix
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A method is presented to solveAx=b by computing optimum iteration parameters for Richardson's method, which supplements the Manteuffel algorithm, developed for the Chebyshev case.Abstract:
A method is presented to solveAx=b by computing optimum iteration parameters for Richardson's method. It requires some information on the location of the eigenvalues ofA. The algorithm yields parameters well-suited for matrices for which Chebyshev parameters are not appropriate. It therefore supplements the Manteuffel algorithm, developed for the Chebyshev case. Numerical examples are described.read more
Citations
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Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Book
Iterative Methods for Linear and Nonlinear Equations
TL;DR: Preface How to Get the Software How to get the Software Part I.
Journal ArticleDOI
Krylov Subspace Methods on Supercomputers
TL;DR: An overview of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers and polynomial preconditioning as an alternative to standard incomplete factorization techniques is given.
Journal ArticleDOI
A Hybrid GMRES algorithm for nonsymmetric linear systems
TL;DR: A new hybrid iterative algorithm is proposed for solving large nonsymmetric systems of linear equations that avoids eigenvalue estimates and frequently outperforms the restarted GMRES algorithm.
Journal ArticleDOI
Quasi-kernel polynomials and their use in non-Hermitian matrix iterations
TL;DR: Two quasi-minimal residual methods for solving non-Hermitian linear systems have been proposed, which — unlike GMRES — are based on short recurrences and hence can be used as true iterative schemes, without restarts.
References
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Journal ArticleDOI
An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix
TL;DR: A particular class of regular splittings of not necessarily symmetric M-matrices is proposed, if the matrix is symmetric, this splitting is combined with the conjugate-gradient method to provide a fast iterative solution algorithm.
Journal ArticleDOI
Calculation of Gauss quadrature rules
Gene H. Golub,John H. Welsch +1 more
TL;DR: In this paper, two algorithms for generating the Gaussian quadrature rule defined by the weight function are presented, assuming that the three term recurrence relation is known for the orthogonal polynomials generated by the weighted function.
Journal ArticleDOI
A class of first order factorization methods
TL;DR: A class of first order factorization methods for the solution of large, symmetric, sparse systems of equations is introduced and results from numerical experiments are presented and comparisons with other iterative and direct methods are carried out.