Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators

In this paper, we propose a numerical method to verify bounds for multiple eigenvalues for elliptic eigenvalue problems. We calculate error bounds for approximations of multiple eigenvalues and base functions of the corresponding invariant subspaces. For matrix eigenvalue problems, Rump (Linear Algebra Appl. 324 (2001) 209) recently proposed a validated numerical method to compute multiple eigenvalues. In this paper, we extend his formulation to elliptic eigenvalue problems, combining it with a method developed by one of the authors (Jpn. J. Indust. Appl. Math. 16 (1998) 307).