Abstract
This paper presents a third order iterative method for obtaining the Moore–Penrose and Drazin inverses with a computational cost of O(n3), where n∈N. The performance of the new approach is compared with other methods discussed in the literature. The results show that the algorithm is remarkably efficient and accurate. Furthermore, sufficient criteria in the fractional sense are presented, both for smooth and non-smooth solutions. The fractional elliptic Poisson and fractional sub-diffusion equations in the Caputo sense are considered as prototype examples. The results can be extended to other scientific areas involving numerical linear algebra.
Highlights
Computing the inverse matrix, for a high dimension, has been a time consuming task
We find in the published literature a number of different iterative methods for computing the Moore–Penrose inverse
For computing the inverse of a matrix and based on Method (22), the producers is presented in Algorithm 1
Summary
For a high dimension, has been a time consuming task. Numerical methods are important for the calculation of the inverse of a matrix, and numerical iterative algorithms have a special role among the available techniques. The Moore–Penrose inverse of a matrix A ∈ Cm×n, denoted by A† ∈ Cn×m, is the unique matrix X that obeys the four conditions [1]. Published: 6 October 2021 where A∗ is the conjugate transpose of A. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. We find in the published literature a number of different iterative methods for computing the Moore–Penrose inverse. The most common approach for the approximate inverse, A−1, is the Newton’s iterative method (N M): Vr+1 = Vr(2I − AVr), r = 0, 1, 2, · · · ,
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