On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems
TLDR
In this article, it was shown that the generalized conjugate-gradient (CC) can be simplified if a nonsingular matrix H is available such that HA = ATH.About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-07-01 and is currently open access. It has received 73 citations till now. The article focuses on the topics: Conjugate gradient method & Identity matrix.read more
Citations
More filters
MT3DMS: A Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems; Documentation and User's Guide
Chunmiao Zheng,P P Wang +1 more
TL;DR: MT3DMS as discussed by the authors is the next generation of the modular three-dimensional transport model, with significantly expanded capabilities, including the addition of a third-order total-variation-diminishing (TVD) scheme for solving the advection term that is mass conservative but does not introduce excessive numerical dispersion and artificial oscillation.
Journal ArticleDOI
Recent computational developments in krylov subspace methods for linear systems
TL;DR: Many advances in the development of Krylov subspace methods for the iterative solution of linear systems during the last decade and a half are reviewed.
Journal ArticleDOI
A taxonomy for conjugate gradient methods
TL;DR: It is shown that any CG method for $Ax = b$ is characterized by an hpd inner product matrix B and a left preconditioning matrix C and how eigenvalue estimates may be obtained from the iteration parameters, generalizing the well-known connection between CG and Lanczos.
Journal ArticleDOI
A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part II
TL;DR: It is shown how the cure for exact breakdown can be extended to near-breakdown in such a way that (in exact arithmetic) the well-conditioned formal orthogonal polynomials and the corresponding Krylov space vectors do not depend on the threshold specifying the near- breakdown.
Journal ArticleDOI
Lanczos-type Solvers for Nonsymmetric Linear Systems of Equations
TL;DR: This review article introduces the reader to the basic forms of the Lanczos process and some of the related theory, but also describes in detail a number of solvers that are based on it, including those that are considered to be the most efficient ones.
References
More filters
Journal ArticleDOI
Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
TL;DR: A class of iterative algorithms for solving systems of linear equations where the coefficient matrix is nonsymmetric with positive-definite symmetric part, modelled after the conjugate gradient method, are considered.
Book ChapterDOI
Conjugate gradient methods for indefinite systems
TL;DR: Conjugate gradient methods have often been used to solve a variety of numerical problems, including linear and nonlinear algebraic equations, eigenvalue problems, and minimization problems as discussed by the authors.
Solution of systems of linear equations by minimize iteration
TL;DR: In this paper, the authors adopt the general principles of the previous investigation to the specific demands that arise if we are not interested in the complete analysis of a matrix but only in the more special problem of obtaining the solution of a given set of linear equations.
Journal ArticleDOI
Solution of Systems of Linear Equations by Minimized Iterations1
TL;DR: In this article, the authors adopt the general principles of the previous investigation to the specific demands that arise if we are not interested in the complete analysis of a matrix but only in the more special problem of obtaining the solution of a given set of linear equations.
Journal ArticleDOI
Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
TL;DR: It is shown that the method of Arnoldi can be successfully used for solvinglarge unsymmetric eigenproblems and bounds for the rates of convergence similar to those for the symmetric Lanczos algorithm are obtained.
Related Papers (5)
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more