Results 291 to 300 of about 59,261 (316)

SOR as a preconditioner II

Applied Numerical Mathematics, 1998
This is the second part of a paper concerned with the use of successive overrelaxation (SOR) as a preconditioner for the nonsymmetric iterative solver GMRES [for the first part see ibid. 18, 431-440 (1995; Zbl 0840.65018)]. The focus of the second part is on parallel implementation issues.
DeLong, M. A., Ortega, J. M.
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Friction and Preconditioners

1995
Many structural analysis problems are concerned with friction contact phenomena. These problems are difficult to formulate and even more to solve because they are governed by multivalued tribological laws and some numerical resolutions can lead to unsymmetric operators.
Frédéric Lebon, Pierre Alart, Philippe Doudet   +2 more
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Additive Schwarz Preconditioners

2002
The symmetric positive definite system arising from a finite element discretization of an elliptic boundary value problem can be solved efficiently using the preconditioned conjugate gradient method (cf. (Saad 1996)). In this chapter we discuss the class of additive Schwarz preconditioners, which has built-in parallelism and is particularly suitable ...
Susanne C. Brenner, L. Ridgway Scott
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Preconditioners Based on Fundamental Solutions

BIT Numerical Mathematics, 2005
A new type of preconditioner is used in solving systems of linear algebraic equations obtained from the finite difference discretization of partial differential equations. This preconditioner is a discretization of an approximate inverse given by a convolution-like operator with the fundamental solution as a kernel.
Brandén, H., Sundqvist, P.
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Circulant Preconditioners

2004
Abstract A circulant matrix is a special form of Toeplitz matrix where each row of the matrix is a circular shift of its preceding row; see (1.6). Because of the periodicity, circulant systems can be solved efficiently via a deconvolution by discrete Fast Fourier Transforms (FFTs); see Section 3.2.1.
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Some Aspects of Circulant Preconditioners

SIAM Journal on Scientific Computing, 1993
If \(T\) is a given \(n\times n\) Hermitian Toeplitz matrix, the circulant matrix \(C_ 0\) is determined which minimizes \(\| I-C^{-1/2}TC^{- 1/2}\|_ F\) among all circulant matrices \(C\). It is shown that \(C_ 0\) can be computed in \(O(n\log n)\) operations and that the eigenvalues of \(C_ 0^ 1T\) are asymptotically clustered around \(z=1\).
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Newton-Picard preconditioners

2013
For completeness we give the following excerpt from the preprint Potschka et al. [131] here with adaptions in the variable names to fit the presentation in this thesis.
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Optimal and Superoptimal Circulant Preconditioners

SIAM Journal on Matrix Analysis and Applications, 1992
The author investigates preconditioning methods for linear algebraic systems \(Ax=f\) with a dense positive definite matrix \(A\). He calls a conditioning matrix \(C\) optimal if it minimizes \(\| C-A\|\) and superoptimal if it minimizes \(\| I-C^{-1} A\|\), both in the Frobenius norm.
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M-preconditioner for M-matrices

Applied Mathematics and Computation, 2006
The paper deals with the development and analysis of a preconditioner for the conjugate gradient approach to symmetric linear algebraic systems with a nonsingular \(M\)-matrix as coefficient matrix. Numerical results illustrate the convergence behavior of the new preconditioned conjugate gradient method.
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Preconditioner Design via Bregman Divergences

SIAM Journal on Matrix Analysis and Applications
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Andreas A. Bock, Martin S. Andersen
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