Fast estimation of tridiagonal matrices largest eigenvalue

Abstract

This paper proposes a method for speeding up the estimation of the absolute value of largest eigenvalue of an asymmetric tridiagonal matrix based on Power method. An error analysis shows that the proposed method provide errors no greater than the usual Power method. The proposed method involves the computation of the tridiagonal matrix square under analysis, which is performed through a proposed fast algorithm specially tailored for tridiagonal matrices. We perform numerical simulations on Matlab® platform showing the reliability of the method and the claimed speedup using Sylvester-Kac test matrix.