Work

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

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13172849

Authors: Ce Zhang, Bo Zhao, Wenjing Ren, Ruosong Cao, Tao Liu

Institutions: Changchun Guanghua University, Northeastern University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Division of Graduate Education