Block Updates on Truncated ULV Decomposition

Abstract

A truncated ULV decomposition (TULV) of an m×n matrix X of rank k is a decomposition of the form X = U1LV T 1 + E, where U1 and V1 are left orthogonal matrices, L is a k × k non-singular lower triangular matrix and E is an error matrix. Only U1, V1, L, and ?E?F are stored. We propose algorithms for block updating the TULV based upon Block Classical Gram-Schmidt that in [4]. We also use a refinement algorithm that reduces ?E?F, detects rank degeneracy, corrects it and sharpens the approximation. © Springer International Publishing Switzerland 2013.