Abstract
We present a homotopy algorithm for a certain class of two-parameter eigenvalue problems and give theoretical background of the method. We give the definiteness condition which assures existence of the solution of the original two-parameter eigenvalue problem. We show that if the definiteness condition is satisfied, we can trace homotopy curves starting from n^2 points which can be easily computed, and can reach eigenvalues of the original two-parameter eigenvalue problem. The method is particularly suitable for parallel computation.
