@article{ZVMMF_2004_44_11_a1,
author = {E. F. Galba and V. S. Deineka and I. V. Sergienko},
title = {Limit representation of weighted pseudoinverse matrixes with singular weights and the regularization problems},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1928--1946},
year = {2004},
volume = {44},
number = {11},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_11_a1/}
}
TY - JOUR AU - E. F. Galba AU - V. S. Deineka AU - I. V. Sergienko TI - Limit representation of weighted pseudoinverse matrixes with singular weights and the regularization problems JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2004 SP - 1928 EP - 1946 VL - 44 IS - 11 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_11_a1/ LA - ru ID - ZVMMF_2004_44_11_a1 ER -
%0 Journal Article %A E. F. Galba %A V. S. Deineka %A I. V. Sergienko %T Limit representation of weighted pseudoinverse matrixes with singular weights and the regularization problems %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2004 %P 1928-1946 %V 44 %N 11 %U http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_11_a1/ %G ru %F ZVMMF_2004_44_11_a1
E. F. Galba; V. S. Deineka; I. V. Sergienko. Limit representation of weighted pseudoinverse matrixes with singular weights and the regularization problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 44 (2004) no. 11, pp. 1928-1946. http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_11_a1/
[1] Ward J. F., Bouillon T. L., Lewis T. O., “Weighted pseudoinverses with singular weights”, SIAM J. Appl. Math., 21:3 (1971), 480–482 | DOI | MR | Zbl
[2] Moore E. H., “On the reciprocal of the general algebraic matrix”, Abstract Bull. Amer. Math. Soc., 26 (1920), 394–395
[3] Penrose R., “A generalized inverse for matrices”, Proc. Cambridge Philos. Soc., 51:3 (1955), 406–413 | DOI | MR | Zbl
[4] Albert A., Regressiya, psevdoinversiya i rekurrentnoe otsenivanie, Nauka, M., 1977 | MR
[5] Galba E. F., Molchanov I. N., Skopetskii V. V., “Iteratsionnye metody dlya vychisleniya vzveshennoi psevdoobratnoi matritsy s vyrozhdennymi vesami”, Kibernetika i sistemnyi analiz, 1999, no. 5, 150–169 | MR | Zbl
[6] Galba E. F., “Iteratsionnye metody dlya vychisleniya vzveshennogo normalnogo psevdoresheniya s vyrozhdennymi vesami”, Zh. vychisl. matem. i matem. fiz., 39:6 (1999), 882–896 | MR | Zbl
[7] Bellman R., Vvedenie v teoriyu matrits, Nauka, M., 1969 | MR | Zbl
[8] Lancaster P., Rozsa P., “Eigenvectors of $H$-self-adjoint matrices”, Z. angew. Math. und Mech., 64:9 (1984), 439–441 | DOI | MR | Zbl
[9] Ikramov Kh. D., “Ob algebraicheskikh svoistvakh klassov psevdoperestanovochnykh i $H$-samosopryazhennykh matrits”, Zh. vychisl. matem. i matem. fiz., 32:8 (1992), 155–169 | MR
[10] Hearon John Z., “Symmetrizable generalized inverses of symmetrizable matrices”, J. Res. Nat. Bur. Standards B, 71:4 (1967), 229–231 | MR | Zbl
[11] Baksalary J. K., Kala R., “Symmetrizers of matrices”, Linear Algebra and Appl., 35 (1981), 51–62 | DOI | MR | Zbl
[12] Sen S. K., Venkaiah V. Ch., “On symmetrizing a matrix”, Indian J. Pure and Appl. Math., 19:6 (1988), 554–561 | MR | Zbl
[13] Galba E. F., “Vzveshennoe psevdoobraschenie matrits s vyrozhdennymi vesami”, Ukr. matem. zhurnal, 46:10 (1994), 1323–1327 | MR | Zbl
[14] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR
[15] Lankaster P., Teoriya matrits, Nauka, M., 1982 | MR
[16] Voevodin V. V., Kuznetsov Yu. A., Matritsy i vychisleniya, Nauka, M., 1984 | MR | Zbl
[17] Elden L., “A weight pseudoinverse generalized singular values and constrained least squares problems”, BIT, 22:4 (1982), 487–502 | DOI | MR | Zbl
[18] Vaarmann O., Obobschennye obratnye otobrazheniya, Valgus, Tallinn, 1988 | MR
[19] Morozov V. A., Metody regulyarizatsii neustoichivykh zadach, Izd-vo MGU, M., 1987 | MR
[20] Morozov V. A., Regulyarnye metody resheniya nekorrektno postavlennykh zadach, Nauka, M., 1987 | MR
[21] Meleshko V. I., “Primenenie rekurrentnykh optimalnykh otsenok s psevdoobrascheniem v zadachakh identifikatsii”, Avtomatika i telemekhan., 1978, no. 9, 79–89 | MR | Zbl
[22] Meleshko V. I., “Issledovanie ustoichivykh $L$-psevdoobraschenii neogranichennykh zamknutykh operatorov metodom regulyarizatsii”, Differents. ur-niya, 15:5 (1979), 921–935 | MR | Zbl
[23] Louson Ch., Khenson R., Chislennoe reshenie zadach metoda naimenshikh kvadratov, Nauka, M., 1986 | MR
[24] Zhukovskii E. L., Liptser R. Sh., “O rekurrentnom sposobe vychisleniya normalnykh reshenii lineinykh algebraicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 12:4 (1972), 843–857
[25] Golub G. H., “Some modified eigenvalue problems”, SIAM Rev., 15:2 (1973), 318–334 | DOI | MR | Zbl
[26] Golub G. H., Matt V. von, “Quadratically constrained least squares and quadratic problems”, Numer. Math., 59:6 (1991), 561–580 | DOI | MR | Zbl
[27] Arkharov E. B., Shafiev P. A., “Metody regulyarizatsii zadachi svyazannogo psevdoobrascheniya s priblizhennymi dannymi”, Zh. vychisl. matem. i matem. fiz., 43:3 (2003), 347–353 | MR | Zbl