This survey is intended to give an overview of the existing numerical methods and techniques for solving a multi-parameter eigenvalue problem. It also collects some well-known examples of multi-parameter spectral problem and its practical applications in different scientific areas.
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- Atkinson F. V. Multiparameter Eigenvalue Problems. Matrices and Compact Operators. Vol. 1. New York, London, Academic Press (1972).
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- Ji X. Numerical solution of joint eigenpairs of a family of commutative matrices. Appl. Math. Lett. 4 (3), 57--60 (1991).
- Ji X. A two-dimensional bisection method for solving two-parameter eigenvalue problems. SIAM J. Matrix Anal. Appl. 13 (4), 1085–1093 (1992).
- Shimasaki M. Homotopy algorithm for two-parameter eigenvalue problems. Trans Japan SIAM. 5, 121--129 (1995).
- Shimasaki M. Numerical method based on homotopy algorithm for two-parameter problems. Trans Japan SIAM. 6, (1996).
- Plestenjak B. A. A continuation method for a right definite two-parameter eigenvalue problem. SIAM J. Matrix. Anal. Appl. 21 (4), 1163--1184 (2000).