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2021•Unpublished venueRequires access

Examining Possible LU Decompositions

Ly Jacky Nhiayi, Tuyetdong Phan-Yamada

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Abstract

LU decomposition is a fundamental in linear algebra. Numerous tools exists that provide this important factorization. The authors present the conditions for a matrix to have none, one, or infinitely many LU factorizations. In the case where no factorization exists, the authors illustrate how to approximate an LU decomposition by considering LU factorization of nearby matrices.

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What this paper is about

LU decomposition is a fundamental in linear algebra. Numerous tools exists that provide this important factorization. The authors present the conditions for a matrix to have none, one, or infinitely many LU factorizations. In the case where no factorization exists, the authors illustrate how to approximate an LU decomposition by considering LU factorization of nearby matrices.

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Available abstract

LU decomposition is a fundamental in linear algebra. Numerous tools exists that provide this important factorization. The authors present the conditions for a matrix to have none, one, or infinitely many LU factorizations. In the case where no factorization exists, the authors illustrate how to approximate an LU decomposition by considering LU factorization of nearby matrices.

Key concepts: LU decomposition, Incomplete LU factorization, Factorization, Matrix decomposition, Decomposition, Mathematics, Algebra over a field, Linear algebra

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