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1976•SIAM Journal on ComputingRequires access

Fast Parallel Matrix Inversion Algorithms

L. Csanky

Open publisher page 402 citations

Abstract

The parallel arithmetic complexities of matrix inversion, solving systems of linear equations, computing determinants and computing the characteristic polynomial of a matrix are shown to have the same growth rate. Algorithms are given that compute these problems in $O(\log ^2 n)$ steps using a number of processors polynomial in n. (n is the order of the matrix of the problem.)

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What this paper is about

The parallel arithmetic complexities of matrix inversion, solving systems of linear equations, computing determinants and computing the characteristic polynomial of a matrix are shown to have the same growth rate. Algorithms are given that compute these problems in $O(\log ^2 n)$ steps using a number of processors polynomial in n. (n is the order of the matrix of the problem.)

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OpenAlex reports 402 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The parallel arithmetic complexities of matrix inversion, solving systems of linear equations, computing determinants and computing the characteristic polynomial of a matrix are shown to have the same growth rate. Algorithms are given that compute these problems in $O(\log ^2 n)$ steps using a number of processors polynomial in n. (n is the order of the matrix of the problem.)

Key concepts: Inversion (geology), Matrix polynomial, Polynomial matrix, Matrix (chemical analysis), Algorithm, Mathematics, Polynomial, Computer science

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