[PDF][PDF] An algorithm for the generalized singular value decomposition on massively parallel computers
H Park, LM Ewerbring - Proceedings of the 5th international conference …, 1991 - dl.acm.org
H Park, LM Ewerbring
Proceedings of the 5th international conference on Supercomputing, 1991•dl.acm.orgABSTRACT A new algorithm for computing the generalized singular value decomposition
that diagonalizes two matrices is introduced. First, two existing algorithms are studied, one
due to Paige and the other to Hari and Veselic. The former requires only orthogonal plane
transformations, resulting in two matrices with parallel rows. The latter employs nonsingular
(not necessarily orthogonal) transformations to directly diagonalize the two data matrices.
For many applications, it is preferable to be given both the diagonal matrices and the …
that diagonalizes two matrices is introduced. First, two existing algorithms are studied, one
due to Paige and the other to Hari and Veselic. The former requires only orthogonal plane
transformations, resulting in two matrices with parallel rows. The latter employs nonsingular
(not necessarily orthogonal) transformations to directly diagonalize the two data matrices.
For many applications, it is preferable to be given both the diagonal matrices and the …
Abstract
A new algorithm for computing the generalized singular value decomposition that diagonalizes two matrices is introduced. First, two existing algorithms are studied, one due to Paige and the other to Hari and Veselic. The former requires only orthogonal plane transformations, resulting in two matrices with parallel rows. The latter employs nonsingular (not necessarily orthogonal) transformations to directly diagonalize the two data matrices.
For many applications, it is preferable to be given both the diagonal matrices and the transformation matrices explicitly. Our algorithm has the advantages that the nonsingtdar transformation is readily available, computation of transformations is simple, convergence test is efficient in a parallel computing environment, and the condition number of each nonsingular transformation can be controlled. We present implementation results, obtained on a Connection Machine 2, to compare our new algorithm with that of Paige.
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