Geodesic
The use of block symmetries to solve algebraic eigenvalue problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 11, pp. 1614-1624 Cet article a éte moissonné depuis la source Math-Net.Ru

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Some techniques for utilizing the block structure of a number of classes of special matrices are discussed. These structural features consist of intrablock symmetry and antisymmetry. The purpose of this study is to reduce the computing time and memory requirements for solving spectral problems for such matrices. 
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Kh. D. Ikramov. The use of block symmetries to solve algebraic eigenvalue problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 11, pp. 1614-1624. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_11_a1/

[1] Bunse-Gerstner A., Byers R., Mehrmann V., “A quaternion QR-algorithm”, Numer. Math., 55:1 (1989), 83–95 | DOI | MR | Zbl

[2] Lee A., “Centrohermitian and skew-centrohermitian matrices”, Linear Algebra and its Appls., 29 (1980), 205–210 | DOI | MR | Zbl

[3] Van Loan Ch., “A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix”, Linear Algebra and its Appls., 61 (1984), 233–251 | DOI | MR | Zbl

[4] Byers R., “Solving the algebraic Riccati equation with the matrix sign function”, Linear Algebra and its Appls., 85 (1987), 267–279 | DOI | MR | Zbl

[5] Maltsev A. I., Osnovy lineinoi algebry, Nauka, M., 1970

[6] Voevodin V. V., Lineinaya algebra, Nauka, M., 1980 | MR | Zbl

[7] Gantmakher F. R., Teoriya matrits, Nauka, M., 1988 | MR | Zbl

[8] Faddeev D. K., Sominskii I. S., Sbornik zadach po vysshei algebre, Nauka, M., 1977

[9] Ikramov X. D., “O sobstvennykh znacheniyakh proizvedenii kososimmetrichnykh matrits”, Vopr. konstruirovaniya bibliotek programm: sistemnoe i fuktsionalnoe napolnenie, Izd-vo MGU, M., 1990, 96–101

[10] Faddeev D. K., Faddeeva V. N., Vychislitelnye metody lineinoi algebry, Fizmatgiz, M.–L., 1963 | MR | Zbl

[11] Ikramov Kh. D., Nesimmetrichnaya problema sobstvennykh znachenii, Nauka, M., 1990 | MR

[12] Uilkinson Dzh., Algebraicheskaya problema sobstvennykh znachenii, Nauka, M., 1970

[13] Parlett B., Simmetrichnaya problema sobstvennykh znachenii. Chislennye metody, Mir, M., 1983 | MR | Zbl

[14] Cullum J. K., Willoughby R. A., Lanczos algorithms for large symmetric eigenvalue computations, v. 1, Birkhäuser, Basel, 1985 | Zbl

[15] Ikramov X. D., “Chislennoe reshenie matrichnykh uravnenii i simplekticheskaya matrichnaya algebra”, Vychisl. protsessy i sistemy, 5, Nauka, M., 1987, 154–163 | MR

[16] Dongarra J. J., Gabriel J. R., Koelling D. D., Wilkinson J. H., “The eigenvalue problem for Hermitian matrices with time reversal symmetry”, Linear Algebra and its Appls., 60 (1984), 27–42 | DOI | MR | Zbl

[17] Ikramov X. D., “Matrichnye uravneniya i problema sobstvennykh znachenii dlya gamiltonovykh i $J$-simmetrichnykh matrits”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 1990, no. 4 | MR

[18] Ikramov X. D., “Teorema o diagonalizatsii odnogo tipa gamiltonianov s tochki zreniya teorii operatorov v prostranstvakh s indefinitnoi metrikoi”, Zh. vychisl. matem. i matem. fiz., 29:1 (1989), 3–14 | MR

[19] Sagitov M. S., “O diagonalizatsii bozonnogo gamiltoniana v kompleksnom sluchae”, Chisl. analiz: metody, algoritmy, programmy, Izd-vo MGU, M., 1988, 183–191 | MR

[20] Ikramov Kh. D., Chislennye metody dlya simmetrichnykh lineinykh sistem, Nauka, M., 1988 | MR

[21] Pissanetski S., Tekhnologiya razrezhennykh matrits, Mir, M., 1988 | MR

[22] Ikramov Kh. D., Zadachnik po lineinoi algebre, Nauka, M., 1975 | MR

[23] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR