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
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Journal ArticleDOI
Changing the norm in conjugate gradient type algorithms
TL;DR: The relations for the first sequence of methods have to do with Rutishauser’s LR algorithm; those for the second one are based on a generalization of the Schonauer–Weiss smoothing algorithm.
Journal ArticleDOI
Penalty finite element analysis of incompressible flows using element by element solution algorithms
TL;DR: The iterative methods (conjugate gradient and generalized minimum residual method) are compared with the frontal equation solver for efficiency, and the iterative solvers are found to be economical when a large number of equations are to be solved.
Proceedings ArticleDOI
Towards efficient power system state estimators on shared memory computers
J. Nieplocha,Andres Marquez,Vinod Tipparaju,Daniel Chavarría-Miranda,Ross T. Guttromson,H. Huang +5 more
TL;DR: Findings indicate that CG algorithms should be quite effective on multicore processors.
Book ChapterDOI
Iterative methods for nonsymmetric linear systems
TL;DR: A survey of polynomial methods for solving non-symmetric linear systems with an emphasis on generalizations of the classical conjugate gradient method for symmetric problems is presented.
Journal ArticleDOI
Iterative methods for stabilized mixed velocity pressure finite-elements
John Atanga,David J. Silvester +1 more
TL;DR: In this paper, three types of iterative algorithms for solving the Stokes equations are investigated, and the results of numerical experiments are discussed and the applications of these algorithms are given.
References
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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...
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