@article{ZVMMF_1991_31_1_a1,
author = {L. A. Knizhnerman},
title = {Calculation of functions of unsymmetric matrices using {Arnoldi's} method},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {5--16},
year = {1991},
volume = {31},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1991_31_1_a1/}
}
TY - JOUR AU - L. A. Knizhnerman TI - Calculation of functions of unsymmetric matrices using Arnoldi's method JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1991 SP - 5 EP - 16 VL - 31 IS - 1 UR - http://geodesic.mathdoc.fr/item/ZVMMF_1991_31_1_a1/ LA - ru ID - ZVMMF_1991_31_1_a1 ER -
L. A. Knizhnerman. Calculation of functions of unsymmetric matrices using Arnoldi's method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 31 (1991) no. 1, pp. 5-16. http://geodesic.mathdoc.fr/item/ZVMMF_1991_31_1_a1/
[1] Arnoldi W. E., “The principle of minimized iterations in the solution of the matrix eigenvalue problem”, Quart. Appl. Math., 9:1 (1951), 17–29 | MR | Zbl
[2] Saad Y., “Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices”, Linear Algebra and Appl., 34 (1980), 269–295 | DOI | MR | Zbl
[3] Saad Y., “Krylov subspace method for solving large unsymmetric linear systems”, Math. Comput., 37:155 (1981), 105–126 | DOI | MR | Zbl
[4] Elman H. C., Saad Y., Saylor P. E., “A hybrid Chebyshev Krylov subspace algorithm for solving nonsymmetric systems of linear equations”, SIAM J. Sci. and Statist. Comput., 7:3 (1986), 840–855 | DOI | MR | Zbl
[5] Gear C. W., Saad Y., “Iterative solution of linear equations in ODE codes”, SIAM J. Sci. and Statist. Comput., 4:4 (1983), 583–601 | DOI | MR | Zbl
[6] Druskin V. L., Knizhnerman L. A., Ispolzovanie operatornykh ryadov po ortogonalnym mnogochlenam pri vychislenii funktsii ot samosopryazhennykh operatorov i obosnovanie fenomena Lantsosha, Dep. v VINITI 02.03.87, No 1535-V87, 47 pp.
[7] Suetin P. K., Ryady po mnogochlenam Fabera, Nauka, M., 1984 | MR | Zbl
[8] Parlett B., Simmetrichnaya problema sobstvennykh znachenii, Mir, M., 1983 | MR | Zbl
[9] Voevodin V. V., Oshibki okrugleniya i ustoichivost v pryamykh metodakh lineinoi algebry, Izd-vo MGU, M., 1969
[10] Daniel J. W., Gragg W. B., Kaufman L., Stewart G. W., “Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization”, Math. Comput., 30 (1976), 772–795 | MR | Zbl
[11] Householder A. S., The theory of matrices in numerical analysis, Blaisdel Publs Co., N. Y., 1964 | MR | Zbl
[12] Wilkinson G. H., Rounding errors in algebraic process, Prentice-Hall, N. Y., 1964
[13] Uilkinson Dzh. Kh., Rainsh K., Spravochnik algoritmov na yazyke Algol, Mashinostroenie, M., 1976
[14] Lankaster P., Teoriya matrits, Nauka, M., 1978 | MR
[15] Dzyadyk V. K., Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami, Nauka, M., 1977 | MR | Zbl
[16] Navarra A., “An application of the Arnoldi's method to a geophysical fluid dynamics problem”, J. Comput. Phys., 69:1 (1987), 143–162 | DOI | MR | Zbl