Journal ArticleDOI
Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems☆
TLDR
Methods are described for the solution of certain sparse linear systems with a non-symmetric matrix that arises from discretisation of second order partial differential equations with first order derivative terms.About:
This article is published in Journal of Computational Physics.The article was published on 1981-11-01. It has received 121 citations till now. The article focuses on the topics: Matrix-free methods & Symmetric matrix.read more
Citations
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Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
TL;DR: In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist.
Journal ArticleDOI
Preconditioning techniques for large linear systems: a survey
TL;DR: This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices, including progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions.
Journal ArticleDOI
Inverse theory applied to multi‐source cross‐hole tomography.: part 1: acoustic wave‐equation method1
TL;DR: In this article, the use of high speed, high capacity vector computers allows the resultant finite-difference equations to be factored in-place, allowing inversions to be generated using data from a very large number of source positions.
Journal ArticleDOI
Iterative solution of linear systems in the 20th century
TL;DR: In this article, the main research developments in the area of iterative methods for solving linear systems during the 20th century are described and compared, and the most signicant contributions during the past century are compared to one another.
Journal ArticleDOI
An accurate and efficient finite-difference algorithm for non-hydrostatic free-surface flow with application to wave propagation
Guus S. Stelling,Marcel Zijlema +1 more
TL;DR: In this paper, a numerical technique is presented for the approximation of vertical gradient of the non-hydrostatic pressure arising in the Reynolds-averaged Navier-Stokes equations for simulating free-surface flows.
References
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Matrix iterative analysis
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
Journal ArticleDOI
Iterative solution of implicit approximations of multidimensional partial differential equations
TL;DR: In this article, a new iterative method has been developed for solving the large sets of algebraic equations that arise in the approximate solution of multidimensional partial differential equations by implicit numerical techniques.
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.
Related Papers (5)
An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more