Article

Null space and eigenspace computations with additive preprocessing

Authors:

Xiaodong YanAuthors Info & Claims

SNC '07: Proceedings of the 2007 international workshop on Symbolic-numeric computation

Pages 152 - 160

https://doi.org/10.1145/1277500.1277523

Published: 25 July 2007 Publication History

Abstract

We propose and analyze additive preprocessing for computing a vector in the null space of a matrix and a basis for this space. Due to our preprocessing, instead of singular linear systems we solve nonsingular ones, which preserve the conditioning properties and the structure of the input matrices. We extend our preprocessing to decrease the size and the condition number of an ill conditioned input matrix. We also cover applications to the eigenspace computations and to generating effective preconditioners for a linear system of equations.

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Cited By

Pan VGrady DMurphy BQian GRosholt RRuslanov A(2008)Schur aggregation for linear systems and determinantsTheoretical Computer Science10.1016/j.tcs.2008.09.005409:2(255-268)Online publication date: 10-Dec-2008
https://dl.acm.org/doi/10.1016/j.tcs.2008.09.005
Pan VMurphy BRosholt RTang YWang XZheng A(2008)Eigen-solving via reduction to DPR1 matricesComputers & Mathematics with Applications10.1016/j.camwa.2007.09.01256:1(166-171)Online publication date: 1-Jul-2008
https://dl.acm.org/doi/10.1016/j.camwa.2007.09.012

Index Terms

Null space and eigenspace computations with additive preprocessing
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices

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cover image ACM Conferences

SNC '07: Proceedings of the 2007 international workshop on Symbolic-numeric computation

July 2007

218 pages

ISBN:9781595937445

DOI:10.1145/1277500

General Chair:
Stephen M. Watt
The University of Western Ontario, Canada
,
Program Chair:
Jan Verschelde
University of Chicago at Illinois

Copyright © 2007 ACM.

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Published: 25 July 2007

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ISSAC07: International Symposium on Symbolic and Algebraic Computation

July 25 - 27, 2007

Ontario, London, Canada

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Cited By

Pan VGrady DMurphy BQian GRosholt RRuslanov A(2008)Schur aggregation for linear systems and determinantsTheoretical Computer Science10.1016/j.tcs.2008.09.005409:2(255-268)Online publication date: 10-Dec-2008
https://dl.acm.org/doi/10.1016/j.tcs.2008.09.005
Pan VMurphy BRosholt RTang YWang XZheng A(2008)Eigen-solving via reduction to DPR1 matricesComputers & Mathematics with Applications10.1016/j.camwa.2007.09.01256:1(166-171)Online publication date: 1-Jul-2008
https://dl.acm.org/doi/10.1016/j.camwa.2007.09.012

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