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

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Publicado en:Mathematics vol. 13, no. 17 (2025), p. 2849-2864
Autor principal: Zhang, Ce
Otros Autores: Zhao, Bo, Ren Wenjing, Cao Ruosong, Liu, Tao
Publicado:
MDPI AG
Materias:
Control theory
Approximation
Iterative algorithms
Methods
Eigenvalues
Convergence
Algorithms
Weighting functions
Iterative methods
Linear algebra
Acceso en línea:Citation/Abstract
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Resumen: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
Fuente:Engineering Database