Abstract

In a complete problem of eigenvalues of matrices of the $n$-th order the essential role is played by the development of the characteristic determinant $$ D(\lambda)=\det(A-\lambda E)$$ or some other determinant which is essentially identical to this one. There is a series of different methods by which we come to the explicit form of this polynomial. In this paper iterative formulas are derived for finding of all eigenvalues of a real matrix without developing the characteristic polynomial. The method is based on the Newton's method for solving systems of nonlinear equations.

Keywords: Iterative method, eigenvalues of matrices.

MSC: 65F15

Pages:  17--21     

Volume  56 ,  Issue  1$-$2 ,  2004