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
Journal ArticleDOI
Orthogonal error methods
Vance Faber,Thomas A. Manteuffel +1 more
TL;DR: This paper describes a class of algorithms that includes both the conjugate gradient algorithms as described in [12] and the orthogonal residual algorithms and characterize the class of matrices for which finite term Orthogonal error algorithms exist.
ReportDOI
NSPCG (Nonsymmetric Preconditioned Conjugate Gradient) user's guide: Version 1. 0: A package for solving large sparse linear systems by various iterative methods
TL;DR: NSPCG (or Nonsymmetric Preconditioned Conjugate Gradient) is a computer package to solve the linear system Au = b by various iterative methods.
Journal ArticleDOI
A historical overview of iterative methods
TL;DR: A historical overview of the development of iterative methods for the solution of large sparse systems of linear equations with emphasis on the use of vector and parallel processors is presented.
Journal ArticleDOI
Necessary and sufficient conditions for the simplification of generalized conjugate-gradient algorithms
Wayne D. Joubert,David M. Young +1 more
TL;DR: In this paper, the authors characterized the cases where ORTHODIR, a generalized conjugate-gradient algorithm for solving complex non-Hermitian linear systems, can be defined by a short recurrence formula and thus simplified.
A look-ahead variant of the Lanczos algorithm and its application to the quasi-minimal residual method for non-Hermitian linear systems. Ph.D. Thesis - Massachusetts Inst. of Technology, Aug. 1991
TL;DR: In this paper, a look-ahead variant of the Lanczos algorithm is proposed, which overcomes the breakdowns by skipping over those steps where a breakdown or a near-breakdown would occur.
References
More filters
Journal ArticleDOI
Methods of Conjugate Gradients for Solving Linear Systems
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.
Journal ArticleDOI
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
TL;DR: In this article, a systematic method for finding the latent roots and principal axes of a matrix, without reducing the order of the matrix, has been proposed, which is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of minimized iterations.
Journal ArticleDOI
The principle of minimized iterations in the solution of the matrix eigenvalue problem
TL;DR: In this paper, an interpretation of Dr. Cornelius Lanczos' iteration method, which he has named ''minimized iterations'' is discussed, expounding the method as applied to the solution of the characteristic matrix equations both in homogeneous and nonhomogeneous form.
Journal ArticleDOI
Solution of Sparse Indefinite Systems of Linear Equations
TL;DR: The method of conjugate gradients for solving systems of linear equations with a symmetric positive definite matrix A is given as a logical development of the Lanczos algorithm for tridiagonalizing...
Related Papers (5)
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more