We associate a multiparameter spectral problem in a real Euclidean space with a variational problem of finding a minimum of a certain functional. We establish the equivalence of the spectralproblem and the variational problem. On the basis of the gradient procedure, we propose a numerical algorithm for the determination of its eigenvalues and eigenvectors. The local convergence of the algorithm is proved.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 9, pp. 1247–1256, September, 2009.
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Podlevs’kyi, B.M. Variational approach to the solution of linear multiparameter eigenvalue problems. Ukr Math J 61, 1475–1486 (2009). https://doi.org/10.1007/s11253-010-0290-1
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DOI: https://doi.org/10.1007/s11253-010-0290-1