AN ACCURATE PRODUCT SVD ALGORITHM

被引：15

作者：

BOJANCZYK, AW

EWERBRING, LM

LUK, FT

VANDOOREN, P

机构：

[1] Cornell University, School of Electrical Engineering, Ithaca

[2] Argonne National Laboratory, Mathematics and Computer Science Division, Argonne

[3] Cornell University, School of Electrical Engineering, Ithaca

[4] Philips Research Laboratory, B-1348 Louvain-la-Neuve

来源：

SIGNAL PROCESSING | 1991年 / 25卷 / 02期

关键词：

SINGULAR VALUE DECOMPOSITION (SVD); HK-SVD; SVD OF A MATRIX PRODUCT; JACOBI-SVD ALGORITHM; BACKWARD ERROR ANALYSIS;

D O I：

10.1016/0165-1684(91)90062-N

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

In this paper, we propose a new algorithm for computing a singular value decomposition of a product of three matrices. We show that our algorithm is numerically desirable in that all relevant residual elements will be numerically small.

引用

页码：189 / 201

页数：13

共 12 条

[1]

Charlier, Vanbegin, Van Dooren, On efficient implementations of Kogbetliantz's algorithm for computing the singular value decomposition, Numer. Math., 52, pp. 279-300, (1988)

[2]

De Moor, Golub, Generalized singular value decompositions: A proposal for a standardized nomenclature, Manuscript NA-89-05, (1989)

[3]

Ewerbring, A new generalization of the singular value decomposition: Algorithms and applications, Ph.D. dissertation, (1989)

[4]

Ewerbring, Luk, Canonical correlations and generalized SVD: Applications and new algorithms, J. Comput. Appl. Math., 27, pp. 37-52, (1989)

[5]

Ewerbring, Luk, Computing the singular value decomposition on the Connection Machine, IEEE Trans. Comput., 39, pp. 152-155, (1990)

[6]

Ewerbring, Luk, The HK singular value decomposition of rank-deficient matrix triplets, Report MCS-P125-0190, (1990)

[7]

Fernando, Hammarling, A product induced singular value decomposition for two matrices and balanced realisation, Linear Algebra in Signals, Systems and Control, pp. 128-140, (1988)

[8]

Heath, Laub, Paige, Ward, Computing the SVD of a product of two matrices, SIAM Journal on Scientific and Statistical Computing, 7, pp. 1147-1159, (1986)

[9]

Luk, A triangular processor array for computing singular values, Lin. Algebra Appl., 77, pp. 259-273, (1986)

[10]

Luk, Park, A proof of convergence for two parallel Jacobi SVD algorithms, IEEE Trans. Comput., 38, pp. 806-811, (1989)

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