A fast and efficient Newton-type iterative scheme to find the sign of a matrix-Reference-Cited by-同舟云学术

A fast and efficient Newton-type iterative scheme to find the sign of a matrix

Published:2023 Issue:8 Volume:8 Page:19264-19274
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ullah Malik Zaka¹,Alaslani Sultan Muaysh¹,Mallawi Fouad Othman¹,Ahmad Fayyaz²,Shateyi Stanford³,Asma Mir⁴

Affiliation:

1. Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

2. Department of Mathematics, School of Science, National Textile University, Faisalabad, Pakistan

3. Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa

4. Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia

Abstract

<abstract><p>This work proposes a new scheme under the umbrella of iteration methods to compute the sign of an invertible matrix. To this target, a review of the exiting solvers of the same type is given and then a new scheme is derived based on a multi-step Newton-type nonlinear equation solver. It is shown that the new method and its reciprocal converge globally with wider convergence radii in contrast to their competitors of the same order from the general Padé schemes. After investigation on the theoretical parts, numerical experiments based on complex matrices of various sizes are furnished to reveal the superiority of the proposed solver in terms of elapsed CPU time.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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