On the Compression of Low Rank Matrices

Authors:
H. Cheng;Z. Gimbutas;P. G. Martinsson;V. Rokhlin
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2005

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Abstract

A procedure is reported for the compression of rank-deficient matrices. A matrix A of rank k is represented in the form $A = U \circ B \circ V$, where B is a $k\times k$ submatrix of A, and U, V are well-conditioned matrices that each contain a $k\times k$ identity submatrix. This property enables such compression schemes to be used in certain situations where the singular value decomposition (SVD) cannot be used efficiently. Numerical examples are presented.