A degenerate kernel method for eigenvalue problems of non-compact operators with applications in electromagnetism and continuum-of-alleles models
Hassan Majidian, Esmail Babolian · arXiv (Cornell University) · 2008
We consider the eigenvalue problem of certain kind of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method is used to approximate isolated eigenvalues. It is shown that entries of the corresponding matrix of this method can be evaluated exactly. The convergence of the method is proved; it is proved that the convergence rate is $O(h)$. By some numerical examples, we confirm the results.