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9. LU Factorization and Linear Equations

Nicholas John Higham

Open publisher page 2 citations

Abstract

It appears that Gauss and Doolittle applied the method only to symmetric equations. More recent authors, for example, Aitken, Banachiewicz, Dwyer, and Crout … have emphasized the use of the method, or variations of it, in connection with non-symmetric problems … Banachiewicz … saw the point … that the basic problem is really one of matrix factorization, or “decomposition” as he called it.

About this research paper

What this paper is about

It appears that Gauss and Doolittle applied the method only to symmetric equations. More recent authors, for example, Aitken, Banachiewicz, Dwyer, and Crout … have emphasized the use of the method, or variations of it, in connection with non-symmetric problems … Banachiewicz … saw the point … that the basic problem is really one of matrix factorization, or “decomposition” as he called it.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

It appears that Gauss and Doolittle applied the method only to symmetric equations. More recent authors, for example, Aitken, Banachiewicz, Dwyer, and Crout … have emphasized the use of the method, or variations of it, in connection with non-symmetric problems … Banachiewicz … saw the point … that the basic problem is really one of matrix factorization, or “decomposition” as he called it.

Key concepts: Gaussian elimination, LU decomposition, Linear system, Factorization, Incomplete LU factorization, System of linear equations, Linear algebra, Gaussian

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