## Computing the Generalized Singular Value Decomposition (1991)

Venue: | SIAM J. Sci. Comput |

Citations: | 19 - 1 self |

### BibTeX

@ARTICLE{Bai91computingthe,

author = {Zhaojun Bai and James W. Demmel},

title = {Computing the Generalized Singular Value Decomposition},

journal = {SIAM J. Sci. Comput},

year = {1991},

volume = {14},

pages = {1464--1486}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present a variation of Paige's algorithm for computing the generalized singular value decomposition (GSVD) of two matrices A and B. There are two innovations. The first is a new preprocessing step which reduces A and B to upper triangular forms satisfying certain rank conditions. The second is a new 2 \Theta 2 triangular GSVD algorithm, which constitutes the inner loop of Paige's algorithm. We present proofs of stability and high accuracy of the 2 \Theta 2 GSVD algorithm, and demonstrate it using examples on which all previous algorithms fail. 1 Introduction The purpose of this paper is to describe a variation of Paige's algorithm [28] for computing the following generalized singular value decomposition (GSVD) introduced by Van Loan [33], and Paige and Saunders [25]. This is also called the quotient singular value decomposition (QSVD) in [8]. Theorem 1.1 Let A 2 IR m\Thetan and B 2 IR p\Thetan have rank(A T ; B T ) = n. 1 Then there are orthogonal matrices U , V and Q su...