Numerical methods for solving multiparameter eigenvalue problems

Abstract

This paper is concerned with the numerical solution of multiparameter eigenvalue problems for matrices which arise in discretization of multiparameter Sturm-Liouville eigenvalue problems in ordinary differential equations. Based on the trace theorem and the differentiability theory of QR decomposition two new algorithms are proposed. The locally quadratic convergence analysis of the methods is given. Some numerical results are presented to illustrate the performance and application of our methods.

Keywords:

• Multiparameter eigenvalue problems
• trace theorem
• QR decomposition
• Newton's method

C.R. Categories:

• G1.3
• G1.7

This work was supported in part by grant from the National Natural Science Foundation of China.

This work was supported in part by grant from the National Natural Science Foundation of China.

Notes

This work was supported in part by grant from the National Natural Science Foundation of China.