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Scalability of k -Tridiagonal Matrix Singular Value Decomposition

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  • Andrei Tănăsescu

    (Computer Science and Engineering Department, Faculty of Automatic Control and Computer Science, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania)

  • Mihai Carabaş

    (Computer Science and Engineering Department, Faculty of Automatic Control and Computer Science, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania)

  • Florin Pop

    (Computer Science and Engineering Department, Faculty of Automatic Control and Computer Science, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania
    National Institute for Research & Development in Informatics—ICI, 011455 Bucharest, Romania)

  • Pantelimon George Popescu

    (Computer Science and Engineering Department, Faculty of Automatic Control and Computer Science, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania)

Abstract

Singular value decomposition has recently seen a great theoretical improvement for k -tridiagonal matrices, obtaining a considerable speed up over all previous implementations, but at the cost of not ordering the singular values. We provide here a refinement of this method, proving that reordering singular values does not affect performance. We complement our refinement with a scalability study on a real physical cluster setup, offering surprising results. Thus, this method provides a major step up over standard industry implementations.

Suggested Citation

  • Andrei Tănăsescu & Mihai Carabaş & Florin Pop & Pantelimon George Popescu, 2021. "Scalability of k -Tridiagonal Matrix Singular Value Decomposition," Mathematics, MDPI, vol. 9(23), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3123-:d:694816
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    References listed on IDEAS

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    1. Luo, Wei-Hua & Gu, Xian-Ming & Yang, Liu & Meng, Jing, 2021. "A Lagrange-quadratic spline optimal collocation method for the time tempered fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 1-24.
    2. Nicky J. Welton & Howard H. Z. Thom, 2015. "Value of Information," Medical Decision Making, , vol. 35(5), pages 564-566, July.
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    Cited by:

    1. Jianrong Chen & Xiangui Kang & Yunong Zhang, 2023. "Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices," Mathematics, MDPI, vol. 11(15), pages 1-18, July.

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