Matrix balancing and robust Monte Carlo algorithm for evaluating dominant eigenpair

Abstract

Matrix balancing may effect the stability of algorithms in matrix computations and the accuracy of computed solutions. In this paper, we first introduce an algorithm for matrix balancing. Then, using Monte Carlo method we propose a robust algorithm to evaluate dominant eigenpair of a given matrix. Finally, several randomly generated examples are presented to show the efficiency of the new method.

Keywords

• Monte Carlo algorithms
• Robust Monte Carlo algorithm
• Markov chain
• Balancing
• Eigenpair
• Large scale matrices