Block Approximation of Tall Sparse Matrices and Block-Givens Rotations

Abstract

Estimation of top singular values is one of the widely used techniques and one of the intensively researched problems in Numerical Linear Algebra and Data Science. We consider here two general questions related to this problem:How top singular values are affected by zeroing out a sparse rectangular block of a matrix? How much top singular values differ from top column norms of a tall sparse non-negative matrix ?