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Comparative study of two algorithms for the calculation of the extreme eigenvalues of large matrices

✍ Scribed by S.J. Sciutto

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
225 KB
Volume
79
Category
Article
ISSN
0010-4655

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✦ Synopsis

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.

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A novel algorithm for calculation of the extreme eigenvalues of large Hermitian matrices
✍ Yuko Okamoto; Humphrey J. Maris πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 661 KB

A new fast algorithm for calculating a few maximum (or minimum) eigenvalues and the corresponding eigenvectors of large N x N Hermitian matrices is presented. The method is based on a molecular dynamics algorithm for N coupled harmonic oscillators. The time step for iteration is chosen so that only