On the Compression of Low Rank Matrices
Hongwei Cheng, Zydrunas Gimbutas, Per‐Gunnar Martinsson, Vladimir Abramovich Rokhlin · SIAM Journal on Scientific Computing · 2005
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.