Block Approximation of Tall Sparse Matrices and Block-Givens Rotations
Alexander Kushkuley
TL;DR
This paper investigates how zeroing out blocks and comparing top singular values to column norms affect tall sparse matrices, providing insights relevant to numerical linear algebra and data science.
Contribution
It introduces new analysis methods for understanding the impact of block approximation and column norms on top singular values of sparse matrices.
Findings
Zeroing out blocks can significantly alter top singular values.
Top singular values are closely related to top column norms in sparse matrices.
Results inform better approximation techniques for large sparse matrices.
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 ?
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Taxonomy
TopicsMatrix Theory and Algorithms · Mathematical Inequalities and Applications · Tensor decomposition and applications