Summary
A gradient technique previously developed for computing the eigenvalues and eigenvectors of the general eigenproblemAx=λBx is generalized to the eigentuple-eigenvector problem\(Ax = \sum\limits_{i = 1}^p {\lambda _i B_i x} \). Among the applications of the latter are (1) the determination of complex (λ,x) forAx=λBx using only real arithmetic, (2) a 2-parameter Sturm-Liouville equation and (3) λ-matrices. The use of complex arithmetic in the gradient method is also discussed. Computational results are presented.
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This research was partially supported by NSF Grants MPS74-13332 and MCS76-09172
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Blum, E.K., Geltner, P.B. Numerical solution of eigentuple-eigenvector problems in Hilbert spaces by a gradient method. Numer. Math. 31, 231–246 (1978). https://doi.org/10.1007/BF01397877
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DOI: https://doi.org/10.1007/BF01397877