@article{ZVMMF_2004_44_3_a2,
author = {L. T. Poznyak},
title = {The {Bazley{\textendash}Fox} method with truncations for solving the eigenvalue problem for a pair of symmetric positive bilinear forms},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {403--420},
year = {2004},
volume = {44},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_3_a2/}
}
TY - JOUR AU - L. T. Poznyak TI - The Bazley–Fox method with truncations for solving the eigenvalue problem for a pair of symmetric positive bilinear forms JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2004 SP - 403 EP - 420 VL - 44 IS - 3 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_3_a2/ LA - ru ID - ZVMMF_2004_44_3_a2 ER -
%0 Journal Article %A L. T. Poznyak %T The Bazley–Fox method with truncations for solving the eigenvalue problem for a pair of symmetric positive bilinear forms %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2004 %P 403-420 %V 44 %N 3 %U http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_3_a2/ %G ru %F ZVMMF_2004_44_3_a2
L. T. Poznyak. The Bazley–Fox method with truncations for solving the eigenvalue problem for a pair of symmetric positive bilinear forms. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 44 (2004) no. 3, pp. 403-420. http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_3_a2/
[1] Guld S. Kh., Variatsionnye metody v zadachakh o sobstvennykh znacheniyakh, Mir, M., 1970 | MR
[2] Weinstein A., Stenger W., Methods of intermediate problems for eigenvalues. Theory and ramifications, Acad. Press, New York, 1972 | MR | Zbl
[3] Fox D. W., Rheinboldt W. C., “Computational methods for determining lower bounds for eigenvalues of operators in Hilbert space”, SIAM Rev., 8:4 (1966), 427–462 | DOI | MR | Zbl
[4] Bazley N. W., Fox D. W., “Methods for lower bounds to frequencies of continuous elastic systems”, Z. angew. Math. und Phys., 17:1 (1966), 1–37 | DOI | Zbl
[5] Brown R. D., “Variational approximation methods for eigenvalues. Convergence theorems”, Proc. Banach Internal. Center. Comput. Math., 13, 1984, 543–558 | MR | Zbl
[6] Brown R. D., “Convergence criteria for Aronszajn's method and for the Bazley-Fox method”, Proc. Roy. Soc. Edinburgh. Sect. A, 108:1/2 (1988), 91–108 | MR | Zbl
[7] Brown R. D., “Monotone convergence theorems for variational triples with applications to intermediate problems”, Proc. Roy. Soc. Edinburgh. Sect. A, 117:1/2 (1991), 39–58 | MR | Zbl
[8] Poznyak L. T., Issledovanie skhodimosti metodov promezhutochnykh problem v probleme sobstvennykh znachenii, Avtoref. dis. ...kand. fiz.-matem. nauk, LOMI AH CSSR, L., 1971
[9] Poznyak L. T., “O skhodimosti metoda Bezli-Foksa v probleme sobstvennykh znachenii odnoi bilineinoi formy otnositelno drugoi”, Zh. vychisl. matem. i matem. fiz., 13:4 (1973), 839–853 | Zbl
[10] Bazley N. W., Fox D. W., “Truncations in the method of intermediate problems for lower bounds to eigenvalues”, J. Res. Nat. Bur. Standards, 65B:2 (1961), 105–111 | MR | Zbl
[11] Bazley N. W., Fox D. W., “Lower bounds to eigenvalues using operator decompositions of the form $B^*B$”, Arch. Ration. Mech. and Analys., 10:4 (1962), 352–360 | DOI | MR | Zbl
[12] Bazley N. W., Börsch-Supan W., Fox D. W., “Lower bounds for eigenvalues of a quadratic form relative to a positive quadratic form”, Arch. Ration. Mech. and Analys., 27:5 (1968), 398–406 | MR
[13] Poznyak L. T., “Novaya protsedura srezaniya v metode Bezli-Foksa”, Zh. vychisl. matem. i matem. fiz., 17:1 (1977), 24–41 | MR | Zbl
[14] Aronszajn N., “Approximations methods for eigenvalues of completely continuous symmetric operators”, Proc. Sympos. on the Spectral Theory and Differential Problems, Res. Foundations (June–July 1950), Stillwater, Okla., 1951, 179–202 | MR
[15] Riss F., Sekefalvi-Nad B., Lektsii po funktsionalnomu analizu, Mir, M., 1979 | MR
[16] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl