Analiza metodelor de factorizare la determinarea valorilor proprii ale operatorilor matriciali [Articol]

Abstract

Developing students’ research and application competences is of great importance. This paper is devoted to the research and analysis of factorization methods to determine the eigenvalue matrix operators. Reference literature largely describes direct methods of determining their values by developing the characteristic polynomial. However, only some calculus formulas are recommended for factorization methods. The work presents two factorization methods, applied in determining the values of the eigenvectors of a matrix: Rutishauser and QR method. To begin with, the concepts of vectors and eigenvalues are given, and then the Rutishauser and QR algorithm methods are described. The idea of the Rutishauser method is to build a string of similar matrixes, so that at the limit, to obtain an upper triangular matrix with the diagonal eigenvalues sought. The QR method is a more efficient variant of the Rutishauser method based on matrix factorization.