A Nyström Method for the Eigenvalue Problem of a Class of Noncompact Operators

Abstract

We consider the eigenvalue problem of certain kind of noncompact linear operators given as the sum of a multiplication and a kernel operator. Under the assumption that there is a unique (up to normalization) positive eigenfunction f _p , we propose a combination of the finite section and Nyström methods for approximation of f _p and the corresponding eigenvalue. It is proved that the proposed method is convergent. Some examples of the problem are solved numerically using the proposed method.

Keywords:

• Continuum-of-alleles model
• Eigenvalue problem
• Finite section method
• Noncompact operator
• Nyström method

AMS Subject Classification:

• 45C05