A guided genetic algorithm for diagonalization of symmetric and Hermitian matrices

Abstract

The eigenvalues and eigenvectors of a matrix have many applications in engineering and science, such us studying and solving structural problems in both the treatment of signal or image processing, and the study of quantum mechanics. One of the most important aspects of an algorithm is the speed of execution, especially when it is used in large arrays. For this reason, in this paper the authors propose a new methodology using a genetic algorithm to compute all the eigenvectors and eigenvalues in real symmetric and Hermitian matrices. The algorithm uses a general-purpose library developed by the authors for genetic algorithms (GALGA). The speed of execution and the influence of population size have been studied. Moreover, the algorithm has been tested in different matrices and population sizes by comparing the speed of execution to the number of the eigenvectors. This new methodology is faster than the previous algorithm developed by the authors and all eigenvectors can be obtained with it. In addition, the performance using the Coope matrix has been tested contrasting the results with another technique published in the scientific literature.