Iterative Methods for the Inclusion of the Inverse Matrix

Marko D. Petković and Miodrag S. Petković
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Marko D. Petković: Faculty of Sciences and Mathematics
Miodrag S. Petković: Faculty of Electronic Engineering

Chapter Chapter 15 in Analysis, Approximation, Optimization: Computation and Applications, 2025, pp 275-285 from Springer

Abstract: Abstract In this chapter we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval iterations. The new method is relied on a suitable matrix identity and a modification of a hyper-power method. This method is also feasible in the case of a full-rank m × n $$m\times n$$ matrix, producing the interval sequence which converges to the Moore–Penrose inverse. It is shown that computational efficiency of the proposed method is equal or higher than the methods of hyper-power’s type. Theoretical results are confirmed by numerical experiments.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-85743-0_15

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DOI: 10.1007/978-3-031-85743-0_15

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