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1995•SIAM Journal on Matrix Analysis and ApplicationsRequires access

A Divide-and-Conquer Algorithm for the Bidiagonal SVD

Ming Gu, Stanley C. Eisenstat

Open publisher page 120 citations

Abstract

The authors present a stable and efficient divide-and-conquer algorithm for computing the singular value decomposition (SVD) of a lower bidiagonal matrix. Previous divide-and-conquer algorithms all suffer from a potential loss of orthogonality among the computed singular vectors unless extended precision arithmetic is used. A generalization that computes the SVD of a lower banded matrix is also presented.

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What this paper is about

The authors present a stable and efficient divide-and-conquer algorithm for computing the singular value decomposition (SVD) of a lower bidiagonal matrix. Previous divide-and-conquer algorithms all suffer from a potential loss of orthogonality among the computed singular vectors unless extended precision arithmetic is used. A generalization that computes the SVD of a lower banded matrix is also presented.

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OpenAlex reports 120 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The authors present a stable and efficient divide-and-conquer algorithm for computing the singular value decomposition (SVD) of a lower bidiagonal matrix. Previous divide-and-conquer algorithms all suffer from a potential loss of orthogonality among the computed singular vectors unless extended precision arithmetic is used. A generalization that computes the SVD of a lower banded matrix is also presented.

Key concepts: Divide and conquer algorithms, Singular value decomposition, Mathematics, Orthogonality, Singular value, Generalization, Algorithm, Matrix (chemical analysis)

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