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
Finite element analysis of viscous incompressible flows using primitive variables
TL;DR: In this paper, an overview of the primitive variable finite element models of viscous, incompressible fluids in three-dimensional enclosures, with emphasis on penalty finite elements models, is presented.
Book ChapterDOI
A Generalized GMRES Iterative Method
TL;DR: A generalization of the GMRES iterative method in which the residual vector is no longer minimized in the 2-norm but in a C-norm, where C is a symmetric positive definite matrix.
Posted Content
GMRES algorithms over 35 years.
TL;DR: In this paper, the GMRES algorithm is used for solving nonsingular linear systems and acceleration strategies and parallel algorithms that are useful for solving challenging problems are discussed. But their convergence is not discussed.
A Parallel WLS S tate Estimator on S hared Memory C omputers
TL;DR: An optimized shar ed memor y ver sion of the conjugate gr adient (CG) algor ithm was found to be competitive to state-of-the-ar t implementation of LU solver s for the SE pr oblem on the SGI Altix.
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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