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

Ce Zhang, Bo Zhao, Wenjing Ren, Ruosong Cao and Tao Liu ()
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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

Mathematics, 2025, vol. 13, issue 17, 1-15

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.

Keywords: matrix sign function; sixth-order iterative methods; rational approximations; convergence; numerical linear algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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