An Improved Diagonal Transformation Algorithm for the Maximum Eigenvalue of Zero Symmetric Nonnegative Matrices

Abstract

The irreducibility of nonnegative matrices is an important condition for the diagonal transformation algorithm to succeed. In this paper, we introduce zero symmetry to replace the irreducibility of nonnegative matrices and propose an improved diagonal transformation algorithm for finding the maximum eigenvalue without any partitioning. The improved algorithm retains all of the benefits of the diagonal transformation algorithm while having fewer computations. Numerical examples are reported to show the efficiency of the proposed algorithm. As an application, the improved algorithm is used to check whether a zero symmetric matrix is an H-matrix.

Keywords

• improved diagonal transformation algorithm
• zero symmetric reducible nonnegative matrices
• maximum eigenvalue
• H-matrix