Efficient computation of tridiagonal matrices largest eigenvalue

摘要

This paper proposes a method for a fast estimation of the largest eigenvalue of an asymmetric tridiagonal matrix. The proposed method is based on the Power method and the computation of the square of the original matrix. The matrix square is computed through a proposed fast algorithm designed specifically for tridiagonal matrices. Implementations for compressed column (CCS) and compressed row storage (CRS) formats are provided, discussed and compared to a standard scientific library. We investigate the roundoff numerical errors, showing that the proposed method provides errors no greater than the usual Power method. We provide numerical results with simulations in C/C++ implementation in order to demonstrate the effectiveness of the proposed method.