Geodesic
Error bounds of two-sided approximations for the Sturm--Liouville problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 1, pp. 73-88

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In the paper, the investigation of two-side approximations method for eigenvalue problem based on the well-known fictitious method is pursued. The expansion of eigenvalues of auxiliary problem in power series by small parameter of continuation irrespective of its sign is proved. Unimprovable error bounds of two-sided approximations are obtained. The conjugate-factorized structure of the problem operator plays the decisive role in obtaining the result. The research is realized on descrete level. 
@article{SJVM_2000_3_1_a4,
     author = {S. B. Sorokin},
     title = {Error bounds of two-sided approximations for the {Sturm--Liouville} problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {73--88},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2000_3_1_a4/}
}
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S. B. Sorokin. Error bounds of two-sided approximations for the Sturm--Liouville problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 1, pp. 73-88. http://geodesic.mathdoc.fr/item/SJVM_2000_3_1_a4/