Journal ArticleDOI
H-Splittings and two-stage iterative methods
Andreas Frommer,Daniel B. Szyld +1 more
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TLDR
In this paper, the convergence of two-stage iterative methods for the solution of linear systems is studied and conditions on the splittings are given so that the two stage method is convergent for any number of inner iterations.Abstract:
Convergence of two-stage iterative methods for the solution of linear systems is studied. Convergence of the non-stationary method is shown if the number of inner iterations becomes sufficiently large. TheR 1-factor of the two-stage method is related to the spectral radius of the iteration matrix of the outer splitting. Convergence is further studied for splittings ofH-matrices. These matrices are not necessarily monotone. Conditions on the splittings are given so that the two-stage method is convergent for any number of inner iterations.read more
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Journal ArticleDOI
On asynchronous iterations
Andreas Frommer,Daniel B. Szyld +1 more
TL;DR: Certain models of asynchronous iterations, using a common theoretical framework, are reviewed, including nonsingular linear systems, nonlinear systems, and initial value problems that arise naturally on parallel computers.
Journal ArticleDOI
Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
TL;DR: Assuming exact arithmetic, this analysis can be used to produce computable criteria to bound the inexactness of the matrix-vector multiplication in such a way as to maintain the convergence of the Krylov subspace method.
Journal ArticleDOI
Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem
Ning Zheng,Jun-Feng Yin +1 more
TL;DR: Numerical experiments show that the proposed methods are efficient and accelerate the convergence performance of the modulus-based matrix splitting iteration methods with less iteration steps and CPU time.
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Modulus‐based synchronous multisplitting iteration methods for linear complementarity problems
Zhong-Zhi Bai,Li-Li Zhang +1 more
TL;DR: Numerical results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation and improve the existing convergence theory.
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Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems
Zhong-Zhi Bai,Li-Li Zhang +1 more
TL;DR: The convergence theory of these modulus-based synchronous two-stage multisplitting iteration methods and their relaxed variants when the system matrix is an H + -matrix is established.
References
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Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
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Nonnegative Matrices in the Mathematical Sciences
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
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Matrix iterative analysis
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
Book
Iterative Solution of Large Linear Systems
TL;DR: The ASM preconditioner B is characterized by three parameters: C0, ρ(E) , and ω , which enter via assumptions on the subspaces Vi and the bilinear forms ai(·, ·) (the approximate local problems).