Geodesic
On the calculation of eigenvalues of a symmetric matrix
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 199-203

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An algorithm is proposed for a relatively fast and highly accurate calculation of several eigenvalues and the corresponding eigenvectors of a large symmetric matrix. Results of numerical experiments are presented in which the nine lowest eigenvalues were calculated for the minus-Laplace operator with zero boundary conditions discretized on various two-dimensional regions using the five-point stencil and a grid with the number of nodes exceeding one million. The calculation of a part of the spectrum of an arbitrary square matrix is discussed. 
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     author = {M. F. Sukhinin},
     title = {On the calculation of eigenvalues of a~symmetric matrix},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {199--203},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a1/}
}
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M. F. Sukhinin. On the calculation of eigenvalues of a symmetric matrix. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 199-203. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a1/