Tanana, Vitaly Pavlovich; Rudakova, Tatiana Nikolaevna The optimum of the M. M. Lavrent’ev method. (English) Zbl 1279.35125 J. Inverse Ill-Posed Probl. 18, No. 8, 935-944 (2010). MSC: 35R30 47A52 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{T. N. Rudakova}, J. Inverse Ill-Posed Probl. 18, No. 8, 935--944 (2010; Zbl 1279.35125) Full Text: DOI
Tanana, V. P.; Sidikova, A. I. On the order-optimality of a method for evaluating unbounded operators and applications of the method. (Russian) Zbl 1240.65280 Sib. Zh. Ind. Mat. 12, No. 3, 130-140 (2009). MSC: 65M30 35K05 35R25 65J10 65J20 47A52 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{A. I. Sidikova}, Sib. Zh. Ind. Mat. 12, No. 3, 130--140 (2009; Zbl 1240.65280)
Tanana, V. P.; Kolesnikova, N. Yu. Error estimation of approximate solutions to one inverse problem for a parabolic equation. (English. Russian original) Zbl 1180.35573 Russ. Math. 53, No. 9, 38-44 (2009); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 9, 46-52 (2009). MSC: 35R30 35A24 65J10 65J20 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{N. Yu. Kolesnikova}, Russ. Math. 53, No. 9, 38--44 (2009; Zbl 1180.35573); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 9, 46--52 (2009) Full Text: DOI
Tanana, V. P.; Bulatova, M. G. Order-optimal methods for the approximation of a piecewise-continuous solution to a certain inverse problem. (English. Russian original) Zbl 1145.65065 Russ. Math. 51, No. 3, 60-67 (2007); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2007, No. 3, 65-72 (2007). Reviewer: Teresa Regińska (Warszawa) MSC: 65M32 35R30 47A52 65J22 35K05 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{M. G. Bulatova}, Russ. Math. 51, No. 3, 60--67 (2007; Zbl 1145.65065); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2007, No. 3, 65--72 (2007) Full Text: DOI
Tanana, V. P. On an estimate for the approximation of a piecewise-continuous solution of a linear operator equation. (Russian) Zbl 1224.65139 Sib. Zh. Ind. Mat. 9, No. 3, 124-138 (2006). MSC: 65J10 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sib. Zh. Ind. Mat. 9, No. 3, 124--138 (2006; Zbl 1224.65139)
Tanana, V. P.; Yaparova, N. M. The order-optimality of the projective regularization method in the solution of conditionally well-posed problems. (Russian. English summary) Zbl 1212.47008 Sib. Zh. Vychisl. Mat. 9, No. 4, 353-368 (2006). MSC: 47A52 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{N. M. Yaparova}, Sib. Zh. Vychisl. Mat. 9, No. 4, 353--368 (2006; Zbl 1212.47008)
Tanana, V. P. Order-optimality of the projection regularization method as applied to conditionally well-posed problems. (English. Russian original) Zbl 1144.47009 Dokl. Math. 74, No. 2, 755-757 (2006); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 410, No. 6, 741-743 (2006). Reviewer: Elena V. Tabarintseva (Chelyabinsk) MSC: 47A52 47A50 47N40 65J20 74F05 PDFBibTeX XMLCite \textit{V. P. Tanana}, Dokl. Math. 74, No. 2, 755--757 (2006; Zbl 1144.47009); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 410, No. 6, 741--743 (2006) Full Text: DOI
Tanana, V. P. On the optimality by order of the projective regularisation method for solution of inverse problems. (Russian) Zbl 1051.65066 Sib. Zh. Ind. Mat. 7, No. 2, 117-132 (2004). Reviewer: V. Grebenev (Novosibirsk) MSC: 65J10 65J22 47A52 65M32 35K05 35R30 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sib. Zh. Ind. Mat. 7, No. 2, 117--132 (2004; Zbl 1051.65066)
Tanana, V. P. A new approach to the concept of optimality of methods for solving ill-posed problems. (English. Russian original) Zbl 1156.65308 Dokl. Math. 68, No. 1, 17-19 (2003); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 391, No. 1, 23-25(2003). MSC: 65J10 65J20 47A52 PDFBibTeX XMLCite \textit{V. P. Tanana}, Dokl. Math. 68, No. 1, 17--19 (2003; Zbl 1156.65308); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 391, No. 1, 23--2 (2003)
Tanana, V. P.; Sevast’yanov, Ya. M. On optimal methods of solving linear equations of the first kind with an approximately given operator. (Russian) Zbl 1065.47006 Sib. Zh. Vychisl. Mat. 6, No. 2, 205-208 (2003). Reviewer: Vladimir N. Grebenev (Novosibirsk) MSC: 47A50 49M30 47A52 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{Ya. M. Sevast'yanov}, Sib. Zh. Vychisl. Mat. 6, No. 2, 205--208 (2003; Zbl 1065.47006)
Tanana, V. P.; Menikhes, L. D. On the regularizability of linear inverse problems in Banach spaces. (Russian. English summary) Zbl 1145.47301 Vestn. Chelyab. Univ., Ser. 3, Mat. Mekh. Inform. 2002, No. 1(6), 38-41 (2002). MSC: 47A52 54E40 65J22 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{L. D. Menikhes}, Vestn. Chelyab. Univ., Ser. 3, Mat. Mekh. Inf. 2002, No. 1(6), 38--41 (2002; Zbl 1145.47301)
Ivanov, V. K.; Vasin, V. V.; Tanana, V. P. Theory of linear ill-posed problems and its applications. Transl., updated and revised from the Russian edition 1978. 2nd ed. (English) Zbl 1037.65056 Inverse and Ill-Posed Problems Series. Utrecht: VSP (ISBN 90-6764-367-X/hbk). xiii, 281 p. (2002). Reviewer: Robert Plato (Berlin) MSC: 65J10 65-02 47A52 65J20 45B05 45Q05 65R20 65R30 65R32 PDFBibTeX XMLCite \textit{V. K. Ivanov} et al., Theory of linear ill-posed problems and its applications. Transl., updated and revised from the Russian edition 1978. 2nd ed. Utrecht: VSP (2002; Zbl 1037.65056)
Tanana, V. P. On a new approach to estimating the error bounds for methods of solving ill-posed problems. (Russian) Zbl 1053.65043 Sib. Zh. Ind. Mat. 5, No. 4, 150-163 (2002). Reviewer: V. Grebenev (Novosibirsk) MSC: 65J20 35R25 47A52 65F22 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sib. Zh. Ind. Mat. 5, No. 4, 150--163 (2002; Zbl 1053.65043)
Tanana, V. P. Necessary and sufficient conditions of convergence of finite-dimensional approximations for \(L\)-regularized solutions of operator equations. (English) Zbl 1005.65052 J. Inverse Ill-Posed Probl. 8, No. 4, 449-457 (2000). Reviewer: Gabriel Dimitriu (Iaşi) MSC: 65J10 65R20 65R30 65J20 47A52 45J05 PDFBibTeX XMLCite \textit{V. P. Tanana}, J. Inverse Ill-Posed Probl. 8, No. 4, 449--457 (2000; Zbl 1005.65052) Full Text: DOI
Tanana, V. P.; Shtarkman, A. A. On convergence of finite-dimensional approximations of \(L\)-regularized solutions. (Russian) Zbl 0961.65051 Sib. Zh. Vychisl. Mat. 3, No. 4, 395-403 (2000). Reviewer: V.I.Pinchukov (Novosibirsk) MSC: 65J10 65J20 47A50 47A52 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{A. A. Shtarkman}, Sib. Zh. Vychisl. Mat. 3, No. 4, 395--403 (2000; Zbl 0961.65051)
Menikhes, L. D.; Tanana, V. P. On convergence criteria for approximations to the regularization method. (English. Russian original) Zbl 0944.47007 Sib. Math. J. 40, No. 1, 110-130 (1999); translation from Sib. Mat. Zh. 40, No. 1, 130-141 (1999). Reviewer: V.Grebenev (Novosibirsk) MSC: 47A50 47A58 49R50 65J10 PDFBibTeX XMLCite \textit{L. D. Menikhes} and \textit{V. P. Tanana}, Sib. Math. J. 40, No. 1, 130--141 (1999; Zbl 0944.47007); translation from Sib. Mat. Zh. 40, No. 1, 130--141 (1999) Full Text: DOI
Menikhes, L. D.; Tanana, V. P. A criterion for convergence of regularization method approximation in Banach spaces. (English. Russian original) Zbl 0960.65062 Dokl. Math. 58, No. 3, 449-451 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 363, No. 5, 599-601 (1998). MSC: 65J10 45B05 65R20 65J20 47A52 65R30 PDFBibTeX XMLCite \textit{L. D. Menikhes} and \textit{V. P. Tanana}, Dokl. Math. 58, No. 3, 599--601 (1998; Zbl 0960.65062); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 363, No. 5, 599--601 (1998)
Menikhes, L. D.; Tanana, V. P. On convergence of approximations in the regularization method and the Tikhonov regularization method on the \(n\)-th order. (English) Zbl 0923.65025 J. Inverse Ill-Posed Probl. 6, No. 3, 243-262 (1998). Reviewer: T.Regińska (Warszawa) MSC: 65J10 65J20 45B05 65R20 65R30 47A50 PDFBibTeX XMLCite \textit{L. D. Menikhes} and \textit{V. P. Tanana}, J. Inverse Ill-Posed Probl. 6, No. 3, 243--262 (1998; Zbl 0923.65025) Full Text: DOI
Menikhes, L. D.; Tanana, V. P. A finite-dimensional approximation for Lavrent’ev’s method. (Russian. English summary) Zbl 0907.65050 Sib. Zh. Vychisl. Mat. 1, No. 1, 60-66 (1998). Reviewer: S.A.Malyugin (Novosibirsk) MSC: 65J10 47A50 65J20 PDFBibTeX XMLCite \textit{L. D. Menikhes} and \textit{V. P. Tanana}, Sib. Zh. Vychisl. Mat. 1, No. 1, 60--66 (1998; Zbl 0907.65050)
Tanana, V. P. Methods for solving operator equations. (English) Zbl 0899.65034 Inverse and Ill-posed Problems Series. Utrecht: VSP. 223 p. (1997). MSC: 65Jxx 65-02 47J25 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, Methods for solving operator equations. Utrecht: VSP (1997; Zbl 0899.65034)
Menikhes, L. D.; Tanana, V. P. A convergence criterion for approximations in the residual method in Banach spaces. (English) Zbl 0885.65059 J. Inverse Ill-Posed Probl. 5, No. 3, 255-264 (1997). Reviewer: R.Lepp (Tallinn) MSC: 65J10 65J20 47A50 PDFBibTeX XMLCite \textit{L. D. Menikhes} and \textit{V. P. Tanana}, J. Inverse Ill-Posed Probl. 5, No. 3, 255--264 (1997; Zbl 0885.65059) Full Text: DOI
Tanana, V. P. On approximation of a regularized solution to a nonlinear equation. (English. Russian original) Zbl 0868.41020 Sib. Math. J. 38, No. 2, 360-366 (1997); translation from Sib. Mat. Zh. 38, No. 2, 416-423 (1997). Reviewer: G.N.Dyatlov (Novosibirsk) MSC: 41A65 39B42 47J05 65M30 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sib. Math. J. 38, No. 2, 360--366 (1997; Zbl 0868.41020); translation from Sib. Mat. Zh. 38, No. 2, 416--423 (1997) Full Text: DOI
Tanana, V. P. A convergence criterion for approximations in the residual method for linear ill-posed problems. (English) Zbl 0880.65029 J. Inverse Ill-Posed Probl. 5, No. 2, 193-204 (1997). Reviewer: R.Plato (Berlin) MSC: 65J10 65J20 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, J. Inverse Ill-Posed Probl. 5, No. 2, 193--204 (1997; Zbl 0880.65029) Full Text: DOI
Tanana, V. P.; Tabarintseva, E. V. On a new approach to regularization of ill-posed problems. (English. Russian original) Zbl 0851.47007 Russ. Acad. Sci., Dokl., Math. 49, No. 2, 394-397 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 335, No. 5, 565-566 (1994). Reviewer: Y.Kato (Sakai / Osaka) MSC: 47A50 34G10 35R25 47E05 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{E. V. Tabarintseva}, Russ. Acad. Sci., Dokl., Math. 49, No. 2, 565--566 (1994; Zbl 0851.47007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 335, No. 5, 565--566 (1994)
Tanana, V. P. On a condition for minimality of locally convex spaces in the solution of ill-posed problems. (English. Russian original) Zbl 0827.47009 Russ. Acad. Sci., Dokl., Math. 48, No. 3, 475-477 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 333, No. 2, 155-156 (1993). MSC: 47A50 46A03 35R25 PDFBibTeX XMLCite \textit{V. P. Tanana}, Russ. Acad. Sci., Dokl., Math. 48, No. 3, 1 (1993; Zbl 0827.47009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 333, No. 2, 155--156 (1993)
Ivanov, V. K.; Tanana, V. P. On the well-posedness of conditionally well-posed problems in locally convex spaces. (English. Russian original) Zbl 0833.47008 Russ. Acad. Sci., Dokl., Math. 46, No. 1, 165-168 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 325, No. 6, 1107-1110 (1992). MSC: 47A50 35R25 PDFBibTeX XMLCite \textit{V. K. Ivanov} and \textit{V. P. Tanana}, Russ. Acad. Sci., Dokl., Math. 46, No. 1, 1 (1992; Zbl 0833.47008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 325, No. 6, 1107--1110 (1992)
Tanana, V. P.; Rudakova, T. N. The estimation of the error of the regularization method for ill-posed problems with noninjective operator. (English) Zbl 0785.65068 Tikhonov, Andrej N. (ed.) et al., Ill-posed problems in natural sciences. Proceedings of the international conference held in Moscow (Russia), August 19-25, 1991. Utrecht: VSP. 184-190 (1992). MSC: 65J10 65J20 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{T. N. Rudakova}, in: Ill-posed problems in natural sciences. Proceedings of the international conference held in Moscow (Russia), August 19-25, 1991. Utrecht: VSP; Moscow: TVP Science Publishers. 184--190 (1992; Zbl 0785.65068)
Tanana, V. P.; Rudakova, T. N. On error estimation for the optimal method of solution of incorrect problems in the Hilbert spaces in case of additional constraints upon the error of the operator. (Russian) Zbl 0798.65068 Vestn. Chelyab. Univ., Ser. Mat. Mekh. 1, No. 1, 108-112 (1991). Reviewer: A.Filinkov (Adelaide) MSC: 65J10 65J20 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{T. N. Rudakova}, Vestn. Chelyab. Univ., Ser. Mat. Mekh. 1, No. 1, 108--112 (1991; Zbl 0798.65068)
Tanana, V. P.; Rudakova, T. N. Optimality investigation of the regularization method for problems with the non-injective operator. (Russian) Zbl 0798.65067 Vestn. Chelyab. Univ., Ser. Mat. Mekh. 1, No. 1, 105-108 (1991). Reviewer: A.Filinkov (Adelaide) MSC: 65J10 65J20 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{T. N. Rudakova}, Vestn. Chelyab. Univ., Ser. Mat. Mekh. 1, No. 1, 105--108 (1991; Zbl 0798.65067)
Tanana, V. P.; Yanchenko, S. I. On optimization of regularization methods for singular operator equations of the first kind. (English. Russian original) Zbl 0698.47011 Sov. Math., Dokl. 37, No. 1, 42-45 (1988); translation from Dokl. Akad. Nauk SSSR 298, No. 1, 49-52 (1988). Reviewer: N.A.Warsi MSC: 47A50 35R25 65J10 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{S. I. Yanchenko}, Sov. Math., Dokl. 37, No. 1, 42--45 (1988; Zbl 0698.47011); translation from Dokl. Akad. Nauk SSSR 298, No. 1, 49--52 (1988)
Rogozhin, S. A.; Tanana, V. P. An order optimal solution method for degenerate operator equations. (English. Russian original) Zbl 0666.47008 Sov. Math. 32, No. 5, 113-116 (1988); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1988, No. 5(312), 86-88 (1988). MSC: 47A50 PDFBibTeX XMLCite \textit{S. A. Rogozhin} and \textit{V. P. Tanana}, Sov. Math. 32, No. 5, 113--116 (1988; Zbl 0666.47008); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1988, No. 5(312), 86--88 (1988)
Rogozhin, S. A.; Tanana, V. P. A method optimal with respect to the order for solving degenerate operator equations. (Russian) Zbl 0656.47005 Izv. Vyssh. Uchebn. Zaved., Mat. 1988, No. 5(312), 86-88 (1988). Reviewer: Lu Shijie MSC: 47A50 PDFBibTeX XMLCite \textit{S. A. Rogozhin} and \textit{V. P. Tanana}, Izv. Vyssh. Uchebn. Zaved., Mat. 1988, No. 5(312), 86--88 (1988; Zbl 0656.47005)
Tanana, V. P.; Rekant, M. A.; Yanchenko, S. I. Optimization of methods for solving operator equations. (Optimizatsiya metodov resheniya operatornykh uravnenij.) (Russian) Zbl 0699.65040 Sverdlovsk: Izdatel’stvo Ural’skogo Universiteta. 200 p. R. 1.20 (1987). Reviewer: G.Vainikko MSC: 65J10 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana} et al., Optimizatsiya metodov resheniya operatornykh uravnenij (Russian). Sverdlovsk: Izdatel'stvo Ural'skogo Universiteta (1987; Zbl 0699.65040)
Tanana, V. P. Finite-dimensional approximation of the regularization method. (English. Russian original) Zbl 0617.65051 Sov. Math. 30, No. 7, 89-94 (1986); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 7(290), 65-69 (1986). Reviewer: H.Benker MSC: 65J10 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sov. Math. 30, No. 7, 89--94 (1986; Zbl 0617.65051); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 7(290), 65--69 (1986)
Tanana, V. P. Optimization of regularization methods for solutions of degenerate operator equations. (English) Zbl 0646.47010 Sov. Math. 29, No. 9, 106-108 (1985). MSC: 47A50 47B25 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sov. Math. 29, No. 9, 106--108 (1985; Zbl 0646.47010)
Tanana, V. P. On optimality of regularization methods for linear operator equations with an approximately given operator under the condition of nonuniqueness of the solution. (English. Russian original) Zbl 0608.47014 Sov. Math., Dokl. 32, 289-292 (1985); translation from Dokl. Akad. Nauk SSSR 283, 1092-1095 (1985). Reviewer: N.Warsi MSC: 47A50 49J27 35R25 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sov. Math., Dokl. 32, 289--292 (1985; Zbl 0608.47014); translation from Dokl. Akad. Nauk SSSR 283, 1092--1095 (1985)
Tanana, V. P. On optimization of regularization methods for solving degenerate operator equations. (Russian) Zbl 0608.47013 Izv. Vyssh. Uchebn. Zaved., Mat. 1985, No. 9, 75-76 (1985). Reviewer: J.Kolomý MSC: 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, Izv. Vyssh. Uchebn. Zaved., Mat. 1985, No. 9(280), 75--76 (1985; Zbl 0608.47013)
Danilin, A. R.; Tanana, V. P. Necessary and sufficient conditions for the approximations of linear ill- posed problems in a Hilbert space to converge. (English) Zbl 0601.65037 U.S.S.R. Comput. Math. Math. Phys. 24, No. 3, 5-9 (1984). MSC: 65J10 47A50 PDFBibTeX XMLCite \textit{A. R. Danilin} and \textit{V. P. Tanana}, U.S.S.R. Comput. Math. Math. Phys. 24, No. 3, 5--9 (1984; Zbl 0601.65037) Full Text: DOI
Tanana, V. P. Finite-dimensional approximation of the regularization method for solving inverse problems. (English. Russian original) Zbl 0593.41034 Sov. Math., Dokl. 30, 142-144 (1984); translation from Dokl. Akad. Nauk SSSR 277, 557-559 (1984). Reviewer: S.K.Rangarajan MSC: 41A65 47A50 35R25 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sov. Math., Dokl. 30, 142--144 (1984; Zbl 0593.41034); translation from Dokl. Akad. Nauk SSSR 277, 557--559 (1984)
Danilin, A. R.; Tanana, V. P. Necessary and sufficient conditions for convergence of approximations of linear ill-posed problems in Hilbert space. (Russian) Zbl 0562.65034 Zh. Vychisl. Mat. Mat. Fiz. 24, No. 5, 633-639 (1984). Reviewer: G.Vainikko MSC: 65J10 47A50 PDFBibTeX XMLCite \textit{A. R. Danilin} and \textit{V. P. Tanana}, Zh. Vychisl. Mat. Mat. Fiz. 24, No. 5, 633--639 (1984; Zbl 0562.65034)
Tanana, V. P. On order-optimal regularization of linear operator equations under the condition of nonuniqueness of solutions. (English. Russian original) Zbl 0534.35082 Sov. Math., Dokl. 27, 295-297 (1983); translation from Dokl. Akad. Nauk SSSR 269, 37-38 (1983). Reviewer: B.Straughan MSC: 35R25 47A50 65M30 35A05 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sov. Math., Dokl. 27, 295--297 (1983; Zbl 0534.35082); translation from Dokl. Akad. Nauk SSSR 269, 37--38 (1983)
Tanana, V. P. Regularization of incorrect problems with approximately given operator. (Russian) Zbl 0598.65036 Methods for the solution of incorrect problems and their applications, Proc. All-Union Sch.-Semin., Noorus 1982, 129-135 (1982). MSC: 65J10 47A50 PDFBibTeX XML
Tanana, V. P.; Danilin, A. R. Necessary and sufficient conditions for convergence of finite-dimensional approximations of regularized solutions. (English. Russian original) Zbl 0535.41039 Sov. Math., Dokl. 25, 841-842 (1982); translation from Dokl. Akad. Nauk SSSR 264, 1094-1096 (1982). Reviewer: W.Krabs MSC: 41A65 47A55 47A50 65J10 65M30 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{A. R. Danilin}, Sov. Math., Dokl. 25, 841--842 (1982; Zbl 0535.41039); translation from Dokl. Akad. Nauk SSSR 264, 1094--1096 (1982)
Tanana, V. P. Methods for solving operator equations. (Metody resheniya operatornykh uravnenij). (Russian) Zbl 0501.65016 Akademiya Nauk SSSR. Ural’skij Nauchnyj Tsentr. Institut Matematiki i mekhaniki. Moskva: Izdatel’stvo “Nauka”. 160 p. R. 0.95 (1981). MSC: 65Jxx 65-02 47J25 47A50 PDFBibTeX XML
Tanana, V. P.; Korshunov, V. A. Choice of regularization parameter in solving incorrect problems. (English) Zbl 0457.65037 Sib. Math. J. 21, 602-607 (1981). MSC: 65J10 47J25 65R20 45B05 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{V. A. Korshunov}, Sib. Math. J. 21, 602--607 (1981; Zbl 0457.65037) Full Text: DOI
Tanana, V. P.; Korshunov, V. A. Zur Wahl des Regularisierungsparameters bei der Lösung inkorrekter Probleme. (Russian) Zbl 0448.65030 Sib. Mat. Zh. 21, No. 4, 161-168 (1980). MSC: 65J10 47J25 65R20 45B05 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{V. A. Korshunov}, Sib. Mat. Zh. 21, No. 4, 161--168 (1980; Zbl 0448.65030)
Tanana, V. P. Optimal methods for solving ill-posed problems with supplementary information and their application to the solution of the problem of the gamma-probing of boreholes. (Russian) Zbl 0518.65035 Studies in functional analysis, Interuniv. thematic Collect. Artic., Sverdlovsk 1978, 105-121 (1978). MSC: 65J10 PDFBibTeX XML
Tanana, V. P.; Korshunov, V. A.; Shtarkman, A. A. The principle of minimal residuals in the solution of ill-posed problems. (Russian) Zbl 0518.65034 Studies in functional analysis, Interuniv. thematic Collect. Artic., Sverdlovsk 1978, 99-104 (1978). MSC: 65J10 PDFBibTeX XML
Ivanov, V. K.; Vasin, V. V.; Tanana, V. P. Theory of linear ill-posed problems and its applications. (Teoriya linejnykh nekorrektnykh zadach i ee prilozheniya). (Russian) Zbl 0489.65035 Akademiya Nauk SSSR, Ural’skij Nauchnyj Tsentr; Institut Matematiki i Mekhaniki. Moskva: “Nauka”. 206 p. R. 3.00 (1978). MSC: 65J10 65-02 47A50 PDFBibTeX XML
Tanana, V. P.; Korsunov, V. A. The principle of minimal residuals. (English. Russian original) Zbl 0406.65026 Sov. Math., Dokl. 19, 433-436 (1978); translation from Dokl. Akad. Nauk SSSR 239, 800-803 (1978). MSC: 65J10 65R20 82D25 PDFBibTeX XMLCite \textit{V. P. Tanana} and \textit{V. A. Korsunov}, Sov. Math., Dokl. 19, 433--436 (1978; Zbl 0406.65026); translation from Dokl. Akad. Nauk SSSR 239, 800--803 (1978)
Tanana, V. P. On realization of the quasi-solution method. (Russian) Zbl 0391.47006 Izv. Vyssh. Uchebn. Zaved., Mat. 1977, No. 12(187), 108-113 (1978). MSC: 47A50 47A55 65J10 49M15 PDFBibTeX XMLCite \textit{V. P. Tanana}, Izv. Vyssh. Uchebn. Zaved., Mat. 1977, No. 12(187), 108--113 (1978; Zbl 0391.47006)
Tanana, V. P. On an iterative projection algorithm for solving ill posed problems with an approximately specified operator. (English) Zbl 0381.65031 U.S.S.R. Comput. Math. Math. Phys. 17(1977), No. 1, 12-20 (1978). MSC: 65J10 65M30 35R25 PDFBibTeX XMLCite \textit{V. P. Tanana}, U.S.S.R. Comput. Math. Math. Phys. 17, No. 1, 12--20 (1978; Zbl 0381.65031) Full Text: DOI
Tanana, V. N. On a method of optimal order for the solution of operator equations of the first kind with a perturbed operator. (Russian) Zbl 0442.65041 Issled. Sovrem. Mat. Anal., Mat. Zap. 10, No. 2, 133-141 (1977). MSC: 65J10 47A50 47A53 PDFBibTeX XML
Tanana, V. P. On optimal methods for solving illposed problems with an approximately specified operator and error estimates for the methods. (English. Russian original) Zbl 0402.65033 U.S.S.R. Comput. Math. Math. Phys. 17(1977), No. 2, 1-9 (1978); translation from Zh. Vychisl. Mat. Mat. Fiz. 17, 291-297 (1977). MSC: 65J10 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, U.S.S.R. Comput. Math. Math. Phys. 17, No. 2, 1--9 (1977; Zbl 0402.65033); translation from Zh. Vychisl. Mat. Mat. Fiz. 17, 291--297 (1977) Full Text: DOI
Tanana, V. P. On optimal algorithms for operator equations of the first kind with a perturbed operators. (English) Zbl 0399.41031 Math. USSR, Sb. 33, 281-297 (1977). MSC: 41A65 41A35 41A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, Math. USSR, Sb. 33, 281--297 (1977; Zbl 0399.41031) Full Text: DOI
Tanana, V. P. On classifying incorrectly posed problems and optimal methods for their solution. (Russian) Zbl 0391.47007 Izv. Vyssh. Uchebn. Zaved., Mat. 1977, No. 11(186), 100-112 (1977). MSC: 47A50 65J10 PDFBibTeX XMLCite \textit{V. P. Tanana}, Izv. Vyssh. Uchebn. Zaved., Mat. 1977, No. 11(186), 100--112 (1977; Zbl 0391.47007)
Tanana, V. P. Über optimale Algorithmen für Operatorgleichungen erster Art mit gestörtem Operator. (Russian) Zbl 0383.41024 Mat. Sb., N. Ser. 104(146), 314-333 (1977). MSC: 41A65 41A35 41A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, Mat. Sb., Nov. Ser. 104(146), 314--333 (1977; Zbl 0383.41024) Full Text: EuDML
Tanana, V. P. On an optimal algorithm for operator equations of the first kind with a perturbed operator. (English. Russian original) Zbl 0361.65048 Sov. Math., Dokl. 17, 292-295 (1976); translation from Dokl. Akad. Nauk SSSR 226, 1279-1282 (1976). MSC: 65J05 47A50 65K05 35K05 35-04 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sov. Math., Dokl. 17, 292--295 (1976; Zbl 0361.65048); translation from Dokl. Akad. Nauk SSSR 226, 1279--1282 (1976)
Danilin, A. R.; Tanana, V. P. Über die Konvergenz von Projektionsmethoden zur Lösung linearer inkorrekter Probleme. (Russian) Zbl 0435.47021 Mat. Zap., Sverdl. 9, No. 4, 3-13 (1975). MSC: 47A50 65J10 45B05 49M15 PDFBibTeX XMLCite \textit{A. R. Danilin} and \textit{V. P. Tanana}, Mat. Zap., Sverdl. 9, No. 4, 3--13 (1975; Zbl 0435.47021)
Tanana, V. P. Über die Struktur von Klassen gleichmäßiger Regularisation im Hilbertraum. (Russian) Zbl 0435.47020 Mat. Zap., Sverdl. 9, No. 2, 125-131 (1975). MSC: 47A50 65J10 PDFBibTeX XMLCite \textit{V. P. Tanana}, Mat. Zap., Sverdl. 9, No. 2, 125--131 (1975; Zbl 0435.47020)
Tanana, V. P. On a projection-iterative algorithm for operator equations of the first kind with a perturbed operator. (English. Russian original) Zbl 0349.65039 Sov. Math., Dokl. 16, 1364-1366 (1975); translation from Dokl. Akad. Nauk SSSR 224, 1028-1029 (1975). MSC: 65J05 65R20 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sov. Math., Dokl. 16, 1364--1366 (1975; Zbl 0349.65039); translation from Dokl. Akad. Nauk SSSR 224, 1028--1029 (1975)
Tanana, V. P. Iterative Projektionsmethode zur Lösung von Operatorgleichungen erster Art. (Russian) Zbl 0321.65034 Izv. Vyssh. Uchebn. Zaved., Mat. 1975, No. 5(156), 73-77 (1975). MSC: 65J05 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, Izv. Vyssh. Uchebn. Zaved., Mat. 1975, No. 5(156), 73--77 (1975; Zbl 0321.65034)
Vasin, V. V.; Tanana, V. P. Necessary and sufficient conditions for convergence of projection methods for linear unstable problems. (English. Russian original) Zbl 0327.65051 Sov. Math., Dokl. 15, 628-631 (1974); translation from Dokl. Akad. Nauk SSSR 215, 1032-1034 (1974). MSC: 65J05 47A50 47J05 PDFBibTeX XMLCite \textit{V. V. Vasin} and \textit{V. P. Tanana}, Sov. Math., Dokl. 15, 628--631 (1974; Zbl 0327.65051); translation from Dokl. Akad. Nauk SSSR 215, 1032--1034 (1974)
Tanana, V. P. Berechnung der Werte eines unbeschränkten gestörten Operators. (Russian) Zbl 0304.47013 Mat. Zap., Sverdl. 8, No. 4, 91-99 (1974). MSC: 47A50 65D25 45L05 PDFBibTeX XMLCite \textit{V. P. Tanana}, Mat. Zap., Sverdl. 8, No. 4, 91--99 (1974; Zbl 0304.47013)
Tanana, V. P. Über die Stabilität der Methode der Diskrepanzminderung bei der Lösung inkorrekter Probleme. (Russian) Zbl 0295.47017 Izv. Vyssh. Uchebn. Zaved., Mat. 1974, No. 9(148), 75-80 (1974). MSC: 47A50 65J05 45M10 47A53 47Gxx 49M05 PDFBibTeX XMLCite \textit{V. P. Tanana}, Izv. Vyssh. Uchebn. Zaved., Mat. 1974, No. 9(148), 75--80 (1974; Zbl 0295.47017)
Tanana, V. P. Näherungslösung von Operatorgleichungen erster Art in lokal konvexen Räumen. (Russian) Zbl 0268.47020 Izv. Vyssh. Uchebn. Zaved., Mat. 1973, No. 9(136), 70-77 (1973). MSC: 47A50 65J05 PDFBibTeX XMLCite \textit{V. P. Tanana}, Izv. Vyssh. Uchebn. Zaved., Mat. 1973, No. 9(136), 70--77 (1973; Zbl 0268.47020)
Tanana, V. P. Variationsmethoden zur Lösung von Operatorgleichungen erster Art. (Russian) Zbl 0322.47009 Mat. Zap., Sverdl. 8, No. 2, 108-129 (1972). MSC: 47A50 65J05 49R50 PDFBibTeX XMLCite \textit{V. P. Tanana}, Mat. Zap., Sverdl. 8, No. 2, 108--129 (1972; Zbl 0322.47009)
Tanana, V. P. Approximate solution of operator equations of first kind and geometrical properties of Banach spaces. (Russian) Zbl 0224.47005 Izv. Vyssh. Uchebn. Zaved., Mat. 1971, No. 7(110), 81-93 (1971). MSC: 47A50 46B20 PDFBibTeX XMLCite \textit{V. P. Tanana}, Izv. Vyssh. Uchebn. Zaved., Mat. 1971, No. 7(110), 81--93 (1971; Zbl 0224.47005)
Tanana, V. P. Incorrectly posed problems and the geometry of Banach spaces. (English. Russian original) Zbl 0207.44901 Sov. Math., Dokl. 11, 864-867 (1970); translation from Dokl. Akad. Nauk SSSR 193, 43-45 (1970). Reviewer: Srinivasa Swaminathan MSC: 46B20 47A50 PDFBibTeX XMLCite \textit{V. P. Tanana}, Sov. Math., Dokl. 11, 864--867 (1970; Zbl 0207.44901); translation from Dokl. Akad. Nauk SSSR 193, 43--45 (1970)
Vasin, V. V.; Tanana, V. P. Näherungslösung von Operatorgleichungen erster Art. (Russian) Zbl 0301.47019 Mat. Zap., Sverdl. 6, No. 4, 27-37 (1968). MSC: 47A50 65J05 PDFBibTeX XMLCite \textit{V. V. Vasin} and \textit{V. P. Tanana}, Mat. Zap., Sverdl. 6, No. 4, 27--37 (1968; Zbl 0301.47019)