An efficient hyperpower iterative method for computing weighted MoorePenrose inverse

• Main Authors: Manpreet Kaur, Munish Kansal, Sanjeev Kumar
• Format: Article
• Language: English
• Published: AIMS Press 2020-02-01
• Series: AIMS Mathematics
• Subjects: weighted moore-penrose inverse; rank-deficient matrix; hyperpower iterative method; matrix multiplication; generalized inverse
• Online Access: https://www.aimspress.com/article/10.3934/math.2020113/fulltext.html

In this paper, we propose a new hyperpower iterative method for approximating the weighted Moore-Penrose inverse of a given matrix. The main objective of the current work is to minimize the computational complexity of the hyperpower iterative method using some transformations. The proposed method attains the fifth-order of convergence using four matrix multiplications per iteration step. The theoretical convergence analysis of the method is discussed in detail. A wide range of numerical problems is considered from scientific literature, which demonstrates the applicability and superiority of the proposed method.