The solution of Abel's integral equation by a modified broken line of minimum length method

V. I. Gryn'   ; L. V. Nitishinskaya

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 34 (1994) no. 8, pp. 1219-1236

Bibliographie

[1] Piketov V. V., Preobrazhenskii N. G., “O nekotorykh problemakh diagnostiki nizkotemperaturnoi plazmy, reshaemykh s pomoschyu EVM”, Svoistva nizkotemperaturnoi plazmy i metody ee diagnostiki, Nauka, Novosibirsk, 1977, 138–176

[2] Preobrazhenskii N. G., Pikalov V. V., Neustoichivye zadachi diagnostiki plazmy, Nauka, Novosibirsk, 1982

[3] Voskoboinikov Yu. E., Preobrazhenskii N. G., Sedelnikov A. I., Matematicheskaya obrabotka eksperimenta v molekulyarnoi gazodinamike, Nauka, Novosibirsk, 1984

[4] Minerbo G. N., Levy M. E., “Inversion on Abel's integral equation by means of orthogonal polynomials”, SIAM J. Numer. Analys., 6:4 (1969), 598–616 | DOI | MR | Zbl

[5] Kosarev E. L., “O chislennom reshenii integralnogo uravneniya Abelya”, Zh. vychisl. matem. i matem. fiz., 13:6 (1973), 1591–1596 | MR | Zbl

[6] Galker J., Fischer D., “Uber den Einsatz von Spline-Funktionen zur Gläftung von Meßwerten bei der Abel-Inversion”, Ann. Phys., 33:3 (1976), 191–199

[7] Malinowski H., “A numerical method for solving the Abel integral equation”, Zastosov Mat., 16:2 (1978), 275–281 | MR | Zbl

[8] Voskoboinikov Yu. E., “Obraschenie uravneniya Abelya s ispolzovaniem kubicheskikh splainov”, Inversiya Abelya i ee obobscheniya, ITPM SO AN SSSR, Novosibirsk, 1978, 180–189

[9] Voskoboinikov Yu. E., “Kompleks programm dlya sglazhivaniya i differentsirovaniya eksperimentalnykh dannykh pri pomoschi $B$-splainov”, Algoritmich. i apparaturnye sredstva pererabotki informatsii, In-t teplofiz. SO AN SSSR, Novosibirsk, 1981, 43–54

[10] Smarzewski R., Malinovski H., “Numerical solution of a class of Abel integral equations”, J. Inst. Math. Appl., 22 (1978), 159–170 | DOI | MR | Zbl

[11] Marchenko N. A., Pergament A. X., Obrabotka interferogramm na EVM, Preprint No 42, IPMatem. AN SSSR, M., 1982, 28 pp.

[12] Pavlov N. N., “Splainy v vypuklykh mnozhestvakh i uslovnaya korrektnost zadachi resheniya nekotorykh integralnykh uravnenii pervogo roda”, Splainy i vychisl. matem., Vychisl. sistemy, 115, Novosibirsk, 1986, 98–104 | MR

[13] Vershinin V. V., Zavyalov Yu. S., Pavlov N. N., Ekstremalnye svoistva splainov i zadacha sglazhivaniya, Nauka, Novosibirsk, 1988 | MR

[14] Grebennikov A. I., “Regulyarizuyuschie algoritmy resheniya nekotorykh nekorrektnykh zadach s pomoschyu splainov”, Metody i algoritmy v chisl. analize, Izd-vo MGU, M., 1984, 128–140 | MR

[15] Morozov V. A., Metody regulyarizatsii neustoichivykh zadach, Izd-vo MGU, M., 1987 | MR

[16] Morozov V. A., Grebennikov A. I., Metody resheniya nekorrektno postavlennykh zadach. Algoritmicheskii aspekt, Izd-vo MGU, M., 1992 | MR | Zbl

[17] Gryn V. I., “Chislennoe reshenie obratnoi zadachi teorii perenosa izlucheniya s tsilindricheskoi simmetriei”, Soobsch. po prikl. matem., VTs AN SSSR, M., 1987

[18] Pavlov N. I., “Sglazhivayuschie splainy pervoi stepeni”, Splain-approksimatsiya i chisl. analiz., Vychisl. sistemy, 108, Novosibirsk, 1985, 31–36 | MR | Zbl

[19] Belaya N. I., “Algoritm postroeniya optimalnoi po tochnosti proizvodnoi funktsii v klasse $C_{2,L,N}$”, Izv. vuzov. Matematika, 1978, no. 8(195), 31–40 | MR | Zbl

[20] Ivanov V. V., “Ob optimalnykh po tochnosti algoritmakh priblizhennogo resheniya operatornykh uravnenii I roda”, Zh. vychisl. matem. i matem. fiz., 15:1 (1975), 3-11 | Zbl

[21] Belaya N. I., Ivanov V. V., “Ob optimalnykh po tochnosti algoritmakh vosstanovleniya proizvodnykh funktsii nekotorykh klassov”, Zh. vychisl. matem. i matem. fiz., 25:3 (1985), 456–461 | MR | Zbl

[22] Belaya N. I., “Optimalnoe po tochnosti vosstanovlenie proizvodnykh funktsii klassa $C_{2,L^\pm,N,\varepsilon}$”, Optimizatsiya vychislenii i chisl. metody, IK AN USSR, Kiev, 1987, 41–44

[23] Stechkin S. B., Subbotin Yu. N., Splainy v vychislitelnoi matematike, Nauka, M., 1976 | MR | Zbl

[24] Logunov S. L., “Otsenki ustoichivosti dlya reshenii nekotorykh uslovnokorrektnykh zadach na mnozhestve funktsii, udovletvoryayuschikh usloviyu Geldera”, Zh. vychisl. matem. i matem. fiz., 31:6 (1991), 925–929 | MR

[25] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1971 | MR | Zbl

[26] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1981 | MR

[27] Vladimirov V. S., “Osobennosti resheniya uravneniya perenosa”, Zh. vychisl. matem. i matem. fiz., 8:4 (1968), 842–852

[28] Germogenova T. A., Lokalnye svoistva reshenii uravneniya perenosa, Nauka, M., 1986 | MR | Zbl

[29] Gryn V. I., “Ob opredelenii koeffitsienta pogloscheniya pri sfericheskoi simmetrii”, Zh. vychisl. matem. i matem. fiz., 30:9 (1990), 1341–1356 | MR | Zbl