نتایج جستجو برای: backward factored approximate inverse

تعداد نتایج: 189250  

2000
Laurent El Ghaoui

The classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix. First, it assumes that the perturbation is infinitesimally small. Second, it does not take into account the perturbation structure (e.g., Vandermonde). Similarly, the classical notion of the inverse of a matrix neglects the possibility of large, structured perturbations. We d...

Ali Reza Tahavvor Mohammad Amin Ahmadfard Mohammad Javad Kazemzadeh-parsi,

In geometric inverse problems, it is assumed that some parts of domain boundaries are not accessible and geometric shape and dimensions of these parts cannot be measured directly. The aim of inverse geometry problems is to approximate the unknown boundary shape by conducting some experimental measurements on accessible surfaces. In the present paper, the artificial neural network is used to sol...

Journal: :Math. Program. 2016
Jingwei Liang Mohamed-Jalal Fadili Gabriel Peyré

In this paper, we present a convergence rate analysis for the inexact Krasnosel’skĭı– Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration–complexity bounds, and then, under a metric subregularity assumption, we establish local linear convergence for the distance of the iterates to the set of fixed points...

2008
Guillaume Bal Alexandre Jollivet

The theory of inverse transport consists of reconstructing optical properties of a domain of interest from measurements performed at the boundary of the domain. Using the decomposition of the measurement operator into singular components (ballistic part, single scattering part, multiple scattering part), several stability estimates have been obtained that show what may stably be reconstructed f...

Journal: :SIAM J. Matrix Analysis Applications 2000
Wei-Pai Tang Wing Lok Wan

Various forms of sparse approximate inverses (SAI) have been shown to be useful for preconditioning. Their potential usefulness in a parallel environment has motivated much interest in recent years. However, the capability of an approximate inverse in eliminating the local error has not yet been fully exploited in multigrid algorithms. A careful examination of the iteration matrices of these ap...

1996
Michele Benzi

1. Introduction. In this note we consider the solution of large, sparse linear systems of

2005
J. Cerdàn

To solve a large, and sparse linear system Ax = b; (1) an approximate solution of (1) is usually obtained by using a preconditioned iterative Krylov subspace method [6]. In this work we focus on factorized approximate inverse preconditioners, in this class of preconditioners two matrices such that its product is an approximation of the inverse of A are computed and stored explicitely. Therefore...

1995
J. A. Scott

We investigate the use of sparse approximate-inverse preconditioners for the iterative solution of unsymmetric linear systems of equations. Such methods are of particular interest because of the considerable scope for parallelization. We propose a number of enhancements which may improve their performance. When run in a sequential environment, these methods can perform unfavourably when compare...

Journal: :SIAM J. Scientific Computing 2000
Michele Benzi Miroslav Tuma

The innuence of reorderings on the performance of factorized sparse approximate inverse preconditioners is considered. Some theoretical results on the eeect of orderings on the ll-in and decay behavior of the inverse factors of a sparse matrix are presented. It is shown experimentally that certain reorderings, like Minimum Degree and Nested Dissection, can be very beneecial both in the precondi...

Journal: :Advances in Engineering Software 2015
Jirí Kopal Miroslav Rozlozník Miroslav Tuma

It is well-known that analysis of incomplete Cholesky and LU decompositions with a general dropping is very difficult and of limited applicability, see, for example, the results on modified decompositions [1], [2], [3] and later results based on similar concepts. This is true not only for the dropping based on magnitude of entries but it also applies to algorithms that use a prescribed sparsity...

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