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 by 2 triangular GSVD algorithm, which constitutes the inner loop of Paige's algorithm. We present proofs of stability and high accuracy of the 2 by 2 GSVD algorithm, and demonstrate it using examples on which all previous algorithms fail.
Keywords: generalized singular value decomposition, CS decomposition, matrix decomposition, Jacobi algorithm, Kogbetliantz algorithm
Title
Computing the Generalized Singular Value Decomposition
Published
1992-12-01
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
CSD-92-720
Type
Text
Extent
22 p
Archive
The Engineering Library
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