Titlebook: Recent Advances in Iterative Methods; Gene Golub,Mitchell Luskin,Anne Greenbaum Conference proceedings 1994 Springer-Verlag New York, Inc.

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Rational Krylov Algorithms for Nonsymmetric Eigenvalue Problems,l iterations with different shifts are started on the same starting vector. Such iterations can be performed in parallel, yielding a . degree Krylov vector in one iteration on . processors. An analogy to a method of experimentally verifying stability of aircraft structures is shown..The algorithm is demonstrated on two applied test problems.

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Highly Parallel Preconditioners for General Sparse Matrices,o introduce a multi-elimination incomplete LU factorization named ILUM, which is related to multifrontal elimination. The main goal of the paper is to discuss some of the prevailing ideas and to compare them on a few test problems.

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,Some Themes in Gene H. Golub’s Work on Iterative Methods, equations. Over the past 30 years, his work has delineated some of the major research directions in these fields, and his visibility and clear exposition of ideas have stimulated an extraordinary amount of interest and research activity by others. In this paper, we review these contributions.

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Computing the Sparse Singular Value Decomposition via SVDPACK,ion ANSI Fortran-77. This software package implements Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left- and right-singular vectors) for large sparse matrices. The package has been ported to a variety of mach

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Gaussian Quadrature Applied to Adaptive Chebyshev Iteration,x .. With the advent of parallel processors, there has been a resurgence of interest in this method. In Chebyshev iteration one determines iteration parameters so that the residual polynomials axe scaled Chebyshev polynomials for some interval [.] on the positive real axis. Chebyshev iteration is of

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Ordering Effects on Relaxation Methods Applied to the Discrete Convection-Diffusion Equation,nal problems, the results show how the performance of iterative solvers is affected by directions of flow associated with the underlying operator. In particular, for problems of size ., relaxation sweeps opposite the direction of flow incur a latency of approximately . steps in which convergence is

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On the Error Computation for Polynomial Based Iteration Methods,metric, positive definite matrix. For both methods we present algorithms which approximate during the iteration process the .th error .. = ||. − ..||.. The algorithms are based on the theory of modified moments and Gaussian quadrature. The proposed schemes are also applicable for other polynomial it

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