Block Approximation of Tall Sparse Matrices and Block-Givens Rotations
arXiv:1707.07799
AI Analysis
Provides theoretical insights for practitioners working with tall sparse matrices in data science and numerical linear algebra.
The paper studies how zeroing out a sparse rectangular block affects top singular values and quantifies the gap between top singular values and top column norms for tall sparse non-negative matrices.
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 ?