KRYLOV AND POWER METHODS FOR EIGENVALUES AND EIGENVECTORS OF A SYMMETRIC MATRIX

Abstract

The article discusses classical methods for finding the eigenvalues and eigenvectors of matrices, such as direct determination using the commands of the mathematical system Mathcad, as well as a two-stage classical method that utilizes the methods of Krylov, and Power methods. For all methods, enlarged algorithms have been built, consisting of a sequence of mathematical formulas and commands of the Mathcad mathematical system. In this case, Mathcad acts as an executor of an enlarged mathematical algorithm for solving the problem.  For all methods, the eigenvalues of the matrices are obtained in four ways: by the method of the internal command Mathcad eigenvals(A),by the internal function of Python, with the help of Python code written for the methods and by the most proposed method. Only if the results of these methods coincide, the enlarged algorithm is considered correct.