The projection Kantorovich method for eigenvalue problems |
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Authors: | LJ Lardy |
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Institution: | Department of Mathematics, Syracuse University, 215 Carnegie Hall, Syracuse, NY 13244-1150, United States |
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Abstract: | A modified projection method for eigenvalues and eigenvectors of a compact operator T on a Banach space is defined and analyzed. The method is derived from the Kantorovich regularization for second-kind equations involving the operator T. It is shown that when T is a positive self-adjoint operator on a Hilbert space and the projections are orthogonal, the modified method always gives eigenvalue approximations which are at least as accurate as those obtained from the projection method. For self-adjoint operators, the required computation is essentially the same for both methods. Numerical computations for two integral operators are presented. One has T positive self-adjoint, while in the other T is not self-adjoint. In both cases the eigenvalue approximations from the modified method are more accurate than those from the projection method. |
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Keywords: | Eigenvalue problems Projection method Kantorovich method |
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