3 edition of **Wavelet sparse approximate inverse preconditioners** found in the catalog.

Wavelet sparse approximate inverse preconditioners

- 261 Want to read
- 32 Currently reading

Published
**1996**
by Research Institute for Advanced Computer Science, NASA Ames Research Center, National Technical Information Service, distributor in [Moffett Field, Calif.], [Springfield, Va
.

Written in English

- Wavelet analysis.,
- Preconditioning.,
- Matrices (Mathematics),
- Iterative solution.,
- Partial differential equations.

**Edition Notes**

Statement | Tony Chan, W.-P. Tang, and W.L. Wan. |

Series | [NASA contractor report] -- NASA-CR-203272., RIACS technical report -- 96.18., NASA contractor report -- NASA CR-203272., RIACS technical report -- TR 96-18. |

Contributions | Tang, W.-P., Wan, W. L., Research Institute for Advanced Computer Science (U.S.) |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL15508593M |

An Improved Wavelet Based Preconditioner for Sparse Linear Problems Discrete Wavelet Transform, Preconditioners, Sparse Matrices, Krylov Subspace Iterative Methods 1. Introduction band of matrix. Later, an approximate form of this can be formed and taken as preconditioner, which controls fill-. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate by:

We propose two sparsity pattern selection algorithms for factored approximate inverse preconditioners to solve general sparse matrices. The sparsity pattern is adaptively updated in the construction phase by using combined information of the inverse and original triangular factors of the original by: 5. An approximate preconditioner with level-by-level wavelets Some analysis and numerical experiments Discussion of the accompanied Mfiles 10 Implicit wavelet preconditioners [T7] Introduction Wavelet-based sparse approximate inverse An implicit wavelet sparse approximate inverse preconditioner

PREF A CE Iterative methods for solving general, large sparse linear systems have been gaining popularity in many areas of scientiﬁc computing. Until recently, direct solution methodsFile Size: 3MB. Home Browse by Title Proceedings IMACS'97 A comparative study of sparse approximate inverse preconditioners ARTICLE A comparative study of sparse approximate inverse preconditioners.

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In their approach, the linear system (1) is first transformed into a standard wavelet basis such as Daubechies the [8] basis, and a sparse approximate inverse preconditioner is computed for the.

We show how to use wavelet compression ideas to improve the performance of approximate inverse preconditioners. Our main idea is to first transform the inverse of the coefficient matrix into a wavelet basis, before applying standard approximate inverse techniques.

In this process, smoothness in the entries ofA −1 are converted into small wavelet coefficients, thus allowing a more Cited by: Wavelet Sparse Approximate Inverse Preconditioners Tony Chan W.-P.

Tang and W. Wan The Research Institute for Advanced Computer Science is operated by Universities Space Research Association, The American (',ity Building, Suite('_olumbia, MD () There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods.

Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g.

Harwell-Boeing collections. Wavelet-based sparse approximate inverse preconditioners are considered for the linear system Ax=b. The preconditioners are good sparse approximations to the inverse of A computed by taking advantage of the compression obtained by working in a wavelet by: 9.

Abstract: In this paper, several preconditioning technique such as symmetric successive overrelaxation (SSOR), block diagonal matrix, sparse approximate inverse and wavelet based sparse approximate inverse are applied to conjugate gradient (CG) method for solving the dense matrix equations from the mixed potential integral equation (MPIE).

Wavelet-based sparse approximate inverse preconditioners are considered for the linear system Ax=b. The preconditioners are good sparse approximations to the inverse of A computed by taking. The standard incomplete LU (ILU) preconditioners often fail for general Wavelet sparse approximate inverse preconditioners book indefinite matrices because they give rise to "unstable" factors L and U.

In such cases, it may be attractive to approximate the inverse of the matrix directly. This paper focuses on approximate inverse preconditioners based on minimizing ||I-AM||F, where AM is the preconditioned by: A SPARSE APPROXIMATE INVERSE PRECONDITIONER FOR NONSYMMETRIC LINEAR SYSTEMS MICHELE BENZIyAND MIROSLAV T UMA z SIAM J.

c Society for Industrial and Applied Mathematics Vol. 19, No. 3, pp. {, May Abstract. This paper is concerned with a new approach to preconditioning for large, sparse linear Size: KB. Key words: Preconditioning, Approximate inverses, Sparse matrices, Wavelet. 1 Introduction. Consider solving the linear systems: Ax = b; () where A is large and sparse.

There is an increasing interest in using sparse approximate inverse preconditioners for. A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell.

Abstract In this paper, several preconditioning technique such as symmetric successive overrelaxation (SSOR), block diagonal matrix, sparse approximate inverse and wavelet based sparse approximate inverse are applied to conjugate gradient (CG) method for solving the dense matrix equations from the mixed potential integral equation (MPIE).Author: L.

Mo, R. Chen, E. Yung. There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g.

Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so. Progress In Electromagnetics Research, P 19 Here x denotes the exact solution and x(i) the approximate solution at the ith iteration step.

K is the condition number deﬂned as: K = max‚max min‚min (9) with ‚max the largest and ‚min the smallest eigenvalue of ore, it is possible to obtain information about the convergence of CG.

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners.

The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Wavelet based sparse approximate inverse preconditioners.

We begin with a brief introduction to classical orthogonal wavelet transforms. For a detailed introduction, see [8]. Assuming n= 2N for simplicity, the L-level wavelet transform of a signal x2Rn can be written as a matrix vector product WTx, where (7) W= W 1W W L with L nand WT k.

There are already good books on signal processing Wavelet sparse approximate inverse preconditioners. – () MathSciNet CrossRef Google Scholar.

Grote, T. Huckle, Parallel preconditioning with sparse approximate inverses. B.V. Rathish Kumar, M. Mehra, Wavelet based preconditioners for sparse linear systems. Appl Author: Mani Mehra. Chan et al. have used Discrete Wavelet transform (DWT, usually complete Discrete Wavelet transform (cDWT) is referred as DWT) for improving the performance of sparse approximate inverse preconditioners as proposed by Grote and Huckle.

They dealt with matrices with smooth inverses resulting from 1-D Laplacian operator and linear PDE with Cited by: 8. There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods.

Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing : Tony F. Chan, W.-P. Tang and W. Wan. We remark that approximate inverse techniques rely on the tacit assumption that for a given sparse matrix A, it is possible to ﬁnd a sparse matrix M which is a good approximation of A r, this is not at all obvious, since the inverse of a sparse matrix is usually dense.

There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for Author: Tony F.

Chan, W.P. Tang and W. L. Wan.Get this from a library! Wavelet sparse approximate inverse preconditioners. [Tony Chan; W -P Tang; W L Wan; Research Institute for Advanced Computer Science (U.S.)].An approximate preconditioner with level-by-level wavelets Some analysis and numerical experiments Discussion of the accompanied Mﬁles 10 Implicit wavelet preconditioners [T7] Introduction Wavelet-based sparse approximate inverse An implicit wavelet sparse approximate inverse preconditioner