Geodesic
On certain two-sided analogues of Newton's method for solving nonlinear eigenvalue problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 11, pp. 1819-1829 Cet article a éte moissonné depuis la source Math-Net.Ru

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Iterative algorithms for finding two-sided approximations to the eigenvalues of nonlinear algebraic eigenvalue problems are examined. These algorithms use an efficient numerical procedure for calculating the first and second derivatives of the determinant of the problem. Computational aspects of this procedure as applied to finding all the eigenvalues from a given complex-plane domain in a nonlinear eigenvalue problem are analyzed. The efficiency of the algorithms is demonstrated using some model problems. 
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B. M. Podlevskii. On certain two-sided analogues of Newton's method for solving nonlinear eigenvalue problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 11, pp. 1819-1829. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_11_a1/

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