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

Gorde:
Argitaratua izan da:Mathematics vol. 13, no. 17 (2025), p. 2849-2864
Egile nagusia: Zhang, Ce
Beste egile batzuk: Zhao, Bo, Ren Wenjing, Cao Ruosong, Liu, Tao
Argitaratua:
MDPI AG
Gaiak:
Control theory
Approximation
Iterative algorithms
Methods
Eigenvalues
Convergence
Algorithms
Weighting functions
Iterative methods
Linear algebra
Sarrera elektronikoa:Citation/Abstract
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Laburpena: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.
ISSN:2227-7390
DOI:10.3390/math13172849
Baliabidea:Engineering Database