Discrete least-squares technique for eigenvalues. Part I: The one-dimensional case |
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Authors: | P Žitňan |
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Affiliation: | (1) Computing Centre, Slovak Academy of Sciences, Dúbravská cesta 9, Sk-842 35 Bratislava, Slovak Republic |
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Abstract: | A discrete least-squares technique for computing the eigenvalues of differential equations is presented. The eigenvalue approximations
are obtained in two steps. Firstly, initial approximations of the desired eigenvalues are computed by solving a quadratic
matrix eigenvalue problem resulting from the least-squares method applied to the equation under consideration. Secondly, these
initial approximations, being of sufficient accuracy in some cases, are improved by using the Gauss-Newton method. Results
from numerical experiments are reported that show great efficiency of the proposed technique in solving both regular and singular
one-dimensional problems. The high flexibility of the technique enables one to use also the multidomain approach and the trial
functions not satisfying any of the prescribed boundary conditions. |
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Keywords: | 65L15 65F15 |
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