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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A General Framework for Recursions for Krylov Space Solvers
TL;DR: The general inconsistent OrthoRes algorithm is introduced, which in contrast to the other recursions is also applicable in situations where for some n the iterate xn is not defined due to a so-called pivot breakdown.
Journal ArticleDOI
Mathematical modelling of chemical engineering systems by finite element analysis using PDE/PROTRAN
TL;DR: A particular software package called PDE/PROTRAN that can solve a general class of either time-dependent, steady-state, or eigenvalue type PDEs in two space dimensions is examined from both a theoretical and practical perspective.
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On vector Hankel determinants
TL;DR: In this article, the Sylvester's identity is shown to be not an optimal one and a more effecient alternative one is proposed, since it avoids the use of the Clifford algebra structure.
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Breakdowns and stagnation in iterative methods
TL;DR: This work investigates when iterative methods can stagnate and describes conditions which characterize stagnation, and shows that in some cases stagnation can imply breakdown.
Book ChapterDOI
On the Use of Iterative Methods with Supercomputers for Solving Partial Differential Equations
David M. Young,David R. Kincaid +1 more
TL;DR: The paper describes research in the Center for Numerical Analysis of The University of Texas on the numerical solution of elliptic partial differential equations by descretization methods, with particular attention to the treatment of nonsymmetric systems.
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.
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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.
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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.
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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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