Results 231 to 240 of about 625 (264)

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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BTTB preconditioners for BTTB systems

Numerical Algorithms, 2011
The authors analyze the BTTB system \(T_{m,n}[f]\mathbf{x}=\mathbf{b}\) by the preconditioned conjugate gradient (PCG)method, where \( T_{m,n}[f]\) denotes the \( m \times n\) block Toeplitz matix with \(n \times n\) Toeplitz blocks (BTTB) generated by a \(( 2\pi, 2\pi)\) - periodic continuous function \(f(x,y)\).
Fu-Rong Lin, Chi-Xi Wang
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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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Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner

Numerical Mathematics: Theory, Methods and Applications, 2010
The 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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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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Parallel preconditioners for elliptic PDEs

Proceedings of the 1996 ACM/IEEE conference on Supercomputing, 1996
Iterative schemes for solving sparse linear systems arising from elliptic PDEs are very suitable for efficient implementation on large scale multiprocessors. However, these methods rely heavily on effective preconditioners which must also be amenable to parallelization.
Vivek Sarin, Ahmed H. Sameh
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On the Approximate Cyclic Reduction Preconditioner

SIAM Journal on Scientific Computing, 1999
A preconditioning method for the iterative solution of large sparse systems of equations is introduced which is based on ideas both from ILU preconditioning and from multigrid. A multilevel structure is obtained by using maximal independent sets for graph coarsening.
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Multithreaded Direction Preserving Preconditioners

2014 IEEE 13th International Symposium on Parallel and Distributed Computing, 2014
The 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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SOR as a Preconditioner

1994
We show by experimental results on some convection-diffusion type equations that the SOR iteration may be a promising preconditioner in conjunction with the GMRES method. Our results indicate that it is critical to take several Gauss-Seidel or SOR iterations, rather than just one, and that at least a factor of two improvement over Gauss-Seidel can be ...
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Robust block preconditioners for poroelasticity

Computer Methods in Applied Mechanics and Engineering, 2020
Qingguo Hong, Shuangshuang Chen, Kai Yang   +2 more
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