Numerical Methods for Two Parameter Eigenvalue Problems
Philip A. Browne · 2008
This thesis is concerned with numerical solutions of two parameter eigenvalue problems. We firstly show that the matrix form of two parameter eigenvalue problems can be decoupled using the Kronecker product at the expense of an increase in dimensionality. We then go on to consider Newton’s method and ob-serve that we can obtain quadratic convergence to eigenvectors and eigenvalues for close enough starting values. Subsequently, we derive sufficient conditions for Newton’s method to be applied. In order to test different methods we construct model examples of two parameter eigenvalue problems and also consider a real world three point boundary problem. Finally we look at tensor Rayleigh quo-tient iteration and apply it to model examples. The experiments are conducted in Matlab.