More on modulus based iterative method for solving large and sparse implicit complementarity problem

Authors

• Bharat Kumar, Pandit Dwarka Prasad Mishra Indian Institute of Information Technology, Design & Manufacturing Jabalpur
• Deepmala Deepmala, Pandit Dwarka Prasad Mishra Indian Institute of Information Technology, Design & Manufacturing Jabalpur
• A. K. Das, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Annals of Operations Research

Abstract

This article presents a class of modulus-based relaxation methods to process the large and sparse implicit complementarity problem. By using two positive diagonal matrices, we formulate a fixed-point equation and prove that it is equivalent to implicit complementarity problem. We provide sufficient convergence conditions for the proposed methods when the system matrix is a P-matrix or an -matrix. We discuss the convergence analysis when the system matrix is a nonsingular matrix. We show that the proposed method can process a subclass of -matrix with the help of numerical illustration. Several numerical examples are shown to illustrate the efficacy of the proposed methods which are superior than the earlier version of modulus-based matrix splitting iteration methods in terms of iteration steps and CPU time.

DOI

10.1007/s10479-025-06743-0

Publication Date

1-1-2025

Recommended Citation

Kumar, Bharat; Deepmala, Deepmala; and Das, A. K., "More on modulus based iterative method for solving large and sparse implicit complementarity problem" (2025). Journal Articles. 5465.
https://digitalcommons.isical.ac.in/journal-articles/5465