Results Using Lanczos’ Method for Finding Eigenvalues of Arbitrary Matrices
Robert Todd Gregory · Journal of the Society for Industrial and Applied Mathematics · 1958
The eigenvalues of an arbitrary matrix with complex elements were found in two steps. First, the matrix A was reduced to a tri-diagonal (i.e., Jacobi) matrix J; and second, the eigenvalues of J were computed. In step one the biorthogonal method of Lanezos [1] was used and in step two a method of determinant evaluation (see Frank [2]) was employed. Lanczos' method involves the construction of two biorthogonal sets of vectors xi , x2, * x*,n and yi, Y2, * * * Yn y using the recursion formulas