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A Sixth-Order Iterative Scheme Through Weighted Rational Approximations for Computing the Matrix Sign Function

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Listed:
  • Ce Zhang

    (Modern Educational Technology Center, Changchun Guanghua University, Changchun 130033, China)

  • Bo Zhao

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Wenjing Ren

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Ruosong Cao

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Tao Liu

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

Abstract

This work introduces a sixth-order multi-step iterative algorithm for obtaining the matrix sign function of nonsingular matrices. The presented methodology employs optimized rational approximations combined with strategically formulated weight functions to achieve both computational efficiency and numerical precision. We present a convergence study that includes the analytical derivation of error terms, formally proving the sixth-order convergence characteristics. Numerical simulations substantiate the theoretical results and demonstrate the algorithm’s advantage over current state-of-the-art approaches in terms of both accuracy and computational performance.

Suggested Citation

  • Ce Zhang & Bo Zhao & Wenjing Ren & Ruosong Cao & Tao Liu, 2025. "A Sixth-Order Iterative Scheme Through Weighted Rational Approximations for Computing the Matrix Sign Function," Mathematics, MDPI, vol. 13(17), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2849-:d:1741737
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