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ABS-Based Direct Method for Solving Complex Systems of Linear Equations

Author

Listed:
  • József Abaffy

    (Institute of Applied Mathematics, Óbuda University, Bécsi út 96/b, 1034 Budapest, Hungary)

  • Szabina Fodor

    (Department of Computer Science, Corvinus University of Budapest, Fovám tér 13-15, 1093 Budapest, Hungary)

Abstract

Efficient solution of linear systems of equations is one of the central topics of numerical computation. Linear systems with complex coefficients arise from various physics and quantum chemistry problems. In this paper, we propose a novel ABS-based algorithm, which is able to solve complex systems of linear equations. Theoretical analysis is given to highlight the basic features of our new algorithm. Four variants of our algorithm were also implemented and intensively tested on randomly generated full and sparse matrices and real-life problems. The results of numerical experiments reveal that our ABS-based algorithm is able to compute the solution with high accuracy. The performance of our algorithm was compared with a commercially available software, Matlab’s mldivide (\) algorithm. Our algorithm outperformed the Matlab algorithm in most cases in terms of computational accuracy. These results expand the practical usefulness of our algorithm.

Suggested Citation

  • József Abaffy & Szabina Fodor, 2021. "ABS-Based Direct Method for Solving Complex Systems of Linear Equations," Mathematics, MDPI, vol. 9(19), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2527-:d:651994
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    References listed on IDEAS

    as
    1. Yassine Benia & Marianna Ruggieri & Andrea Scapellato, 2019. "Exact Solutions for a Modified Schrödinger Equation," Mathematics, MDPI, vol. 7(10), pages 1-9, September.
    2. Szabina Fodor & Zoltán Németh, 2019. "Numerical analysis of parallel implementation of the reorthogonalized ABS methods," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 437-454, June.
    3. Lloyd A. Metzler, 1951. "Taxes and Subsidies in Leontief's Input-Output Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 65(3), pages 433-438.
    4. Szabina Fodor, 2001. "Symmetric and Non-Symmetric ABS Methods for Solving Diophantine Systems of Equations," Annals of Operations Research, Springer, vol. 103(1), pages 291-314, March.
    Full references (including those not matched with items on IDEAS)

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