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Numerical solution of eigentuple-eigenvector problems in Hilbert spaces by a gradient method (1978)

Blum, E. K. ; Geltner, P. B.

Springer

Numerische Mathematik 31 (1978), S. 231-246

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ISSN: 0945-3245

Keywords: AMS(MOS): 65F15 ; CR: 5.14

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01397877

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