A Numerical Method for the Solution of the Double Eigenvalue Problem
E. K. Blum, Alice Chang · IMA Journal of Applied Mathematics · 1978
A generalization of the Rayleigh quotient iterative method, called the Minimum Residual Quotient Iteration (MRQI), is derived for the numerical solution of the 2-parameter eigenvalue problem; i.e. to find scalars μ and a corresponding vector x satisfying the following equations, Ax = λB1x + μB2x, ∥x∥ = 1, f(x) = 0, where A and B are n×n real matrices, ∥.∥ denotes the l2 norm and f is a real functional. The method is applied to double eigenvalue problems for ordinary differential equations and computational results are presented.