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Adaptive coefficients iterative method for computing matrix inverse
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AI
DOI：10.1016/j.laa.2025.11.016.png)
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Abstract
En 中文
In this paper, we construct the new iterative method of the form Xk +1 = XkPk(AXk) where Pk is polynomial, for computing the inverse A-1 of a given invertible matrix A is an element of Rnxn. Coefficients of the polynomial Pk in k-th iteration are variable and determined in a way to minimize the Frobenius norm of the error matrix I-AXk+1. The convergence of the new method is investigated, where several theoretical results are proven. The method is compared to the existing iterative methods of the similar type, on a various numerical examples. The results show that the new method outperforms the existing ones for almost all test matrices. Moreover, they suggest that the new method posses almost global convergence. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keywords:
Iterative methods
Inverses
Regular matrices
Convergence
Eigenvalues
Journal
L
IF:
1.1
Papers:
162
Citations:
0