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Comparative study of two algorithms for the calculation of the extreme eigenvalues of large matrices. (English) Zbl 0878.65028
Summary: Two algorithms for the calculation of extreme eigenvalues of large matrices recently presented are compared. The first one is a modification of the well-known power method with Chebyshev iterations to accelerate convergence and an auxiliary procedure capabable of automatically setting all the external parameters, which was developed by us during the year 1991. The second algorithm is an iterative procedure obtained from the discrete-time difference equations for a system of coupled harmonic oscillators. The analysis presented here allows to demonstrate that this second algorithm is essentially identical to ours.
MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
Software:
POWEV; SPARSEM
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References:
[1] Sciutto, S.J., Comput. phys. commun., 77, 95, (1993)
[2] Wilkinson, J.H., The algebraic eigenvalue problem, (1977), Oxford Univ. Press London · Zbl 0258.65037
[3] Sciutto, S.J., Universidad nacional de la plata, (), preprint (1992), reprinted in
[4] Okamoto, Y.; Maris, H.J., Comput. phys. commun., 76, 191, (1993)
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