Simpler is better: a comparative study of randomized pivoting algorithms for CUR and interpolative decompositions

• Published in: Advances in computational mathematics Vol. 49; no. 4
• Main Authors: Dong, Yijun, Martinsson, Per-Gunnar
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2023; Springer Nature B.V; Springer
• Subjects: Algorithms; Comparative studies; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Decomposition; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Matrices (mathematics); Vector spaces; Visualization; CUR decomposition; Low-rank approximation; Column pivoted QR factorization; Randomized numerical linear algebra; 65F55; Rank revealing factorization; Interpolative decomposition

Matrix skeletonizations like the interpolative and CUR decompositions provide a framework for low-rank approximation in which subsets of a given matrix’s columns and/or rows are selected to form approximate spanning sets for its column and/or row space. Such decompositions that rely on “natural” bas...