Abstract
The general eigenvalue problems that arise from vibrational problems treated by the finite element method can be solved suitably by the method of coordinate overrelaxation. To speed up the convergence of the basic algorithm the symmetric coordinate overrelaxation with Chebyshev acceleration was developed. Theoretically the gain of convergence is promising, but this variant is not very satisfactory since a second parameter has to be chosen and since the modified method cannot help in case of adjacent eigenvalues. A surprisingly decisive improvement of the convergence property is yielded by the method of simultaneous group coordinate overrelaxation. Some representative examples illustrate the behaviour of the variants.
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Schwarz, HR. (1976). Praktische Erfahrungen mit Varianten der Koordinatenueberrelaxation zur Loesung von Eigenwertaufgaben. In: Albrecht, J., Collatz, L. (eds) Numerische Behandlung von Differentialgleichungen Band 2. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 31. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5328-6_14
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DOI: https://doi.org/10.1007/978-3-0348-5328-6_14
Publisher Name: Birkhäuser, Basel
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