The parametric least squares technique for λ-non-linear eigenvalue problems

✍ Scribed by P. ſitňan

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 390 KB
• Volume: 153
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(05)80009-4

✦ Synopsis

The parametric least squares technique suitable for computing the eigenvalues of parametrically non-linear eigenvalue problems is presented. The proposed technique consists of eigenvalue parametrization followed by least squares solution of the parametrized problem. The desired cigenvalue approximations are obtained in the following two steps. Firstly, the continuous univariate function F"(~.) is defined by the solution of the corresponding parametrized least squares problem. Secondly, the local minimizers of F"(~.) determining the cigenvalue approximations are computed. Numerical results for a ~.-non-linear eigenvalue problem and a problem with the eigenvalue parameter in the boundary conditions are reported. The high flexibility of the proposed technique also enables one to use the multi-domain approach and trial functions not satisfying any of the prescribed boundary conditions.