A fast singular value decomposition algorithm of general k-tridiagonal matrices

• Published in: Journal of computational science Vol. 31; pp. 1 - 5
• Main Authors: Tănăsescu, Andrei, Popescu, Pantelimon George
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-02-2019
• Subjects: Block diagonalization; k-Tridiagonal matrix; Permutation; Singular value decomposition; 65F50; Block diagonalization; 15A23; Permutation; k-Tridiagonal matrix; 65F15; 15A18; Singular value decomposition
• ISSN: 1877-7503; 1877-7511
• DOI: 10.1016/j.jocs.2018.12.009

•Improvement of any Singular Value Decomposition Black Box Algorithm for k-tridiagonal matrices.•Mathematical proofs.•Complexity analysis.•Numerical experiments confirming the results.
In this article we present a method to speed up the singular value decomposition (SVD) of a general k-tridiagonal matrix using its block diagonalization. We show a O(n3/k3) parallel algorithm over k threads with no synchronization required. We thoroughly analyze its complexity and show that our method can boost the performance of any general SVD algorithm when applied to k-tridiagonal matrices. We present numerical experiments confirming our results.