A Numerical Method for the Solution of the Double Eigenvalue Problem

A generalization of the Rayleigh quotient iterative method,called the Minimum Residual Quotient Iteration (MRQI), is derivedfor the numerical solution of the 2-parameter eigenvalue problem;i.e. to find scalars µ and a corresponding vector x satisfyingthe following equations, Ax = B₁x + µB₂x, ||x|| = 1, f(x) = 0, where A and B are nxn real matrices, ||.|| denotes the l₂ normand f is a real functional. The method is applied to doubleeigenvalue problems for ordinary differential equations andcomputational results are presented.