Results 221 to 230 of about 1,263 (265)
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Applied Numerical Mathematics, 2017
Preconditioning is usually necessary for CG-type iterative algorithms for the solution of large sparse nonsymmetric linear systems. However, many good preconditioners have only marginal intrinsic parallelism -- ILU and SSOR in the natural ordering are essentially sequential algorithms.
DeLong, M. A., Ortega, J. M.
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Preconditioning is usually necessary for CG-type iterative algorithms for the solution of large sparse nonsymmetric linear systems. However, many good preconditioners have only marginal intrinsic parallelism -- ILU and SSOR in the natural ordering are essentially sequential algorithms.
DeLong, M. A., Ortega, J. M.
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A Schwarz Preconditioner for the Cubed-Sphere
SIAM Journal on Scientific Computing, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stephen J. Thomas +3 more
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Some Remarks on a Multigrid Preconditioner
SIAM Journal on Scientific Computing, 1994A class of multilevel preconditioners is studied. A simple proof for optimal estimate of conditioning is given. Numerical examples are presented.
Jinchao Xu, Jinshui Qin
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Preconditioners for block Toeplitz systems based on circulant preconditioners
Numerical Algorithms, 2001The numerical solution of block Toeplitz systems by preconditioned conjugate gradient methods is considered. Two types of preconditioners based on circulant preconditioners are proposed by combining the ideas which are used in the construction of circulant preconditioners with Toeplitz-like preconditioners.
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An approximate BDDC preconditioner
Numerical Linear Algebra with Applications, 2007AbstractThe balancing domain decomposition by constraints (BDDC) preconditioner requires direct solutions of two linear systems for each substructure and one linear system for a global coarse problem. The computations and memory needed for these solutions can be prohibitive if any one system is too large.
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On Inexact Preconditioners for Nonsymmetric Matrices
SIAM Journal on Scientific Computing, 2005Summary: Inexact versions of the block-triangular preconditioners for nonsymmetric matrices of block two-by-two structures presented by \textit{M. F. Murphy, G. H. Golub}, and \textit{A. J. Wathen}[SIAM J. Sci. Comput. 21, No.~6, 1969--1972 (2000; Zbl 0959.65063)] and by \textit{I. C. F. Ipsen} [ibid.
Zhong-Zhi Bai, Michael K. Ng 0001
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Multiresolution Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing, 2001Summary: We introduce a new preconditioner for elliptic partial differential equations (PDEs) on unstructured meshes. Using a wavelet-inspired basis we compress the inverse of the matrix, allowing an effective sparse approximate inverse by solving the sparsity vs. accuracy conflict. The key issue in this compression is to use second generation wavelets
Robert Bridson, Wei-Pai Tang
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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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Design of a Library of Parallel Preconditioners
The International Journal of High Performance Computing Applications, 2000The authors outline the design principles underlying the ParPre library of parallel preconditioners. ParPre is a message-passing library of distributed preconditioners for linear systems, written using MPI and Petsc. It comprises Schwarz methods, Schur system domain decompositioning, various parallel incomplete factorizations, and multilevel methods.
Tony F. Chan, Victor Eijkhout
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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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