Results 301 to 310 of about 52,672 (321)
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Some Aspects of Circulant Preconditioners
SIAM Journal on Scientific Computing, 1993If \(T\) 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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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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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, 1992The 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, 2006The 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 ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andreas A. Bock, Martin S. Andersen
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Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner
Numerical Mathematics: Theory, Methods and Applications, 2010The optimal preconditioner and the superoptimal preconditioner were proposed in 1988 and 1992 respectively. They have been studied widely since then. Recently, Chen and Jin [6] extend the superoptimal preconditioner to a more general case by using the Moore-Penrose inverse.
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Multithreaded Direction Preserving Preconditioners
2014 IEEE 13th International Symposium on Parallel and Distributed Computing, 2014The scalability and robustness of a class of nonoverlapping domain decomposition preconditioners using 2-way nested dissection reordering is studied. We consider two different factorizations: nested and block versions. Both these variants have advantages and disadvantages.
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