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Tanana Vitalii Pavlovich

Publications in Math-Net.Ru

  1. On the uniqueness of the solution to the inverse boundary value problem for the heat equation on a finite time interval

    Trudy Inst. Mat. i Mekh. UrO RAN, 30:1 (2024),  223–236
  2. On the error in determining the protective layer boundary in the inverse heat problem

    Sib. Zh. Ind. Mat., 26:4 (2023),  143–159
  3. Solution of the inverse boundary value problem of heat transfer for an inhomogeneous ball

    Sib. Zh. Vychisl. Mat., 24:3 (2021),  313–330
  4. On reducing the inverse boundary value problem to the synthesis of two ill-posed problems and their solution

    Sib. Zh. Vychisl. Mat., 23:2 (2020),  219–232
  5. Completeness of the system of eigenfunctions of the Sturm–Liouville problem with the singularity

    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:1 (2020),  59–63
  6. Approximate solution of an inverse boundary value problem for a system of differential equations of parabolic type and estimation of the error of this solution

    Trudy Inst. Mat. i Mekh. UrO RAN, 25:3 (2019),  247–264
  7. On improving an error estimate for a nonlinear projective regularization method when solving an inverse boundary value problem

    Eurasian Journal of Mathematical and Computer Applications, 6:3 (2018),  53–74
  8. On the solution of an inverse boundary value problem for composite materials

    Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:4 (2018),  474–488
  9. A numerical solution to a problem of crystal energy spectrum determination by the heat capacity dependent on a temperature

    Eurasian Journal of Mathematical and Computer Applications, 5:1 (2017),  87–94
  10. One approach to the comparison of error bounds at a point and on a set in the solution of ill-posed problems

    Trudy Inst. Mat. i Mekh. UrO RAN, 23:2 (2017),  230–238
  11. About an approximate solution to the Fredholm integral equation of the first kind by the residual method

    Sib. Zh. Vychisl. Mat., 19:1 (2016),  97–105
  12. On estimating the error of an approximate solution caused by the discretization of an integral equation of the first kind

    Trudy Inst. Mat. i Mekh. UrO RAN, 22:1 (2016),  263–270
  13. On solution of solid state physics inverse problem by means of A. N. Tikhonov's regularization method and estimation of the error of this method

    Vestn. YuUrGU. Ser. Vych. Matem. Inform., 5:1 (2016),  35–46
  14. A two-sided error estimate for a regularizing method based on M.M. Lavrent'ev's method

    Trudy Inst. Mat. i Mekh. UrO RAN, 21:1 (2015),  238–249
  15. An error estimate of a regularizing algorithm based of the generalized residual principle when solving integral equations

    Num. Meth. Prog., 16:1 (2015),  1–9
  16. The finite difference approximation for the Tikhonov regularization method of the n-th order

    Vestn. YuUrGU. Ser. Vych. Matem. Inform., 4:1 (2015),  86–98
  17. Estimation of the precision for the Tikhonov regularization method in solving an inverse problem of solid-state physics

    Sib. Zh. Ind. Mat., 17:2 (2014),  125–136
  18. On the optimality of a generalization of M. M. Lavrent'ev's method in the solution of equations with an error in the operator

    Trudy Inst. Mat. i Mekh. UrO RAN, 19:1 (2013),  258–263
  19. Two sided estimation of continuity module of an integral furl type operator

    Vestnik Chelyabinsk. Gos. Univ., 2013, no. 16,  88–93
  20. About the evaluation of inaccuracy of approximate solution of the inverse problem of solid state physics

    Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 5:2 (2013),  72–78
  21. Features of Mathematical Modelling of Hydrodynamic Research of Oil Layers

    Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:3 (2013),  95–103
  22. On point-wise error estimate in solving inverse problems

    Vestn. YuUrGU. Ser. Vych. Matem. Inform., 2:1 (2013),  90–95
  23. On estimating the error of an approximate solution to an overdetermined inverse problem of thermodiagnostics

    Sib. Zh. Ind. Mat., 15:1 (2012),  145–154
  24. On an error estimate for an approximate solution for an inverse problem in the class of piecewise smooth functions

    Trudy Inst. Mat. i Mekh. UrO RAN, 18:1 (2012),  281–288
  25. On estimating the precision of an approximate solution to an inverse thermodiagnostics problem with free boundary

    Sib. Zh. Ind. Mat., 13:1 (2010),  133–139
  26. An order-optimal method for solving an inverse problem for a parabolic equation

    Sib. Zh. Vychisl. Mat., 13:4 (2010),  451–465
  27. An error estimation of an approximate solution of one inverse problem of thermal diagnostics

    Sib. Zh. Vychisl. Mat., 13:1 (2010),  89–100
  28. On the guaranteed accuracy estimate of an approximate solution of one inverse problem of thermal diagnostics

    Trudy Inst. Mat. i Mekh. UrO RAN, 16:2 (2010),  238–252
  29. Error estimation of approximate solutions to one inverse problem for a parabolic equation

    Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 9,  46–52
  30. On the Order Optimality of a Method for Evaluating Unbounded Operators and Its Applications

    Sib. Zh. Ind. Mat., 12:3 (2009),  130–140
  31. Order-optimal methods for the approximation of a piecewise-continuous solution to a certain inverse problem

    Izv. Vyssh. Uchebn. Zaved. Mat., 2007, no. 3,  65–72
  32. On an order-optimal method for solving an inverse problem for a parabolic equation

    Sib. Zh. Ind. Mat., 10:4 (2007),  129–134
  33. On a method to approximate discontinuous solutions of nonlinear inverse problems

    Sib. Zh. Vychisl. Mat., 10:2 (2007),  221–228
  34. On an estimate for the approximation of a piecewise-continuous solution of a linear operator equation

    Sib. Zh. Ind. Mat., 9:3 (2006),  124–138
  35. The optimum in order method of solving conditionally-correct problems

    Sib. Zh. Vychisl. Mat., 9:4 (2006),  353–368
  36. On an optimal method for solving an inverse Stefan problem

    Sib. Zh. Ind. Mat., 8:4 (2005),  124–130
  37. On an approximation method of a discontinuous solution of an ill-posed problem

    Sib. Zh. Ind. Mat., 8:1 (2005),  129–142
  38. On the order-optimality of the projection regularization method in solving inverse problems

    Sib. Zh. Ind. Mat., 7:2 (2004),  117–132
  39. On the convergence of regularized solutions of nonlinear operator equations

    Sib. Zh. Ind. Mat., 6:3 (2003),  119–133
  40. О решении обратной задачи нестационарной фильтрации

    Vestnik Chelyabinsk. Gos. Univ., 2003, no. 9,  5–15
  41. Об оптимальности метода невязки

    Vestnik Chelyabinsk. Gos. Univ., 2003, no. 7,  174–188
  42. Об оптимальности метода установления

    Vestnik Chelyabinsk. Gos. Univ., 2003, no. 7,  165–173
  43. Оптимальные методы решения линейных уравнений первого рода с приближенно заданным оператором

    Vestnik Chelyabinsk. Gos. Univ., 2003, no. 7,  154–164
  44. О регуляризации нелинейных операторных уравнений

    Vestnik Chelyabinsk. Gos. Univ., 2003, no. 7,  5–21
  45. On a new approach to error estimation for methods for solving ill-posed problems

    Sib. Zh. Ind. Mat., 5:4 (2002),  150–163
  46. On solution of an ill-posed problem for a semilinear differential equation

    Sib. Zh. Vychisl. Mat., 5:2 (2002),  189–198
  47. О регуляризуемости линейных обратных задач в банаховых пространствах

    Vestnik Chelyabinsk. Gos. Univ., 2002, no. 6,  38–41
  48. On convergence of finite dimensional approximations of $L$-regularized solutions

    Sib. Zh. Vychisl. Mat., 3:4 (2000),  395–403
  49. On criteria for the convergence of approximations in the regularization method

    Sibirsk. Mat. Zh., 40:1 (1999),  130–141
  50. On the convergence of finite-dimensional approximations of regularized solutions in the theory of nonlinear problems

    Izv. Vyssh. Uchebn. Zaved. Mat., 1998, no. 10,  66–70
  51. The finite-dimensional approximation for the Lavrent'ev method

    Sib. Zh. Vychisl. Mat., 1:1 (1998),  59–66
  52. On the approximate solution of nonlinear operator equations

    Sibirsk. Mat. Zh., 39:5 (1998),  1175–1183
  53. On an approximation of a regularized solution of a nonlinear equation

    Sibirsk. Mat. Zh., 38:2 (1997),  416–423
  54. On a criterion for the convergence of the residual method

    Dokl. Akad. Nauk, 343:1 (1995),  22–24
  55. A new approach to the regularization of ill-posed problems

    Dokl. Akad. Nauk, 335:5 (1994),  565–566
  56. On the minimality condition for locally convex spaces in the solution of ill-posed problems

    Dokl. Akad. Nauk, 333:2 (1993),  155–156
  57. Solution of ill-posed problems in locally convex spaces

    Dokl. Akad. Nauk, 326:2 (1992),  233–236
  58. Well-posedness of conditionally well-posed problems in locally convex spaces

    Dokl. Akad. Nauk, 325:6 (1992),  1107–1110
  59. Об оценке погрешности оптимального метода решения некорректных задач в гильбертовых пространствах при дополнительных ограничениях на погрешность оператора

    Vestnik Chelyabinsk. Gos. Univ., 1991, no. 1,  108–111
  60. Исследование на оптимальность метода регуляризации для задач с неинъективным оператором

    Vestnik Chelyabinsk. Gos. Univ., 1991, no. 1,  105–107
  61. On the optimization of methods for the regularization of degenerate operator equations of the first kind

    Dokl. Akad. Nauk SSSR, 298:1 (1988),  49–52
  62. An order-optimal method for solving degenerate operator equations

    Izv. Vyssh. Uchebn. Zaved. Mat., 1988, no. 5,  86–88
  63. Finite-dimensional approximation of the regularization method

    Izv. Vyssh. Uchebn. Zaved. Mat., 1986, no. 7,  65–69
  64. Optimality of regularization methods for linear operator equations with approximately given operator under the condition of nonuniqueness of the solution

    Dokl. Akad. Nauk SSSR, 283:5 (1985),  1092–1095
  65. Regularization of a one-dimensional inverse problem of filtration in an inhomogeneous stratum

    Dokl. Akad. Nauk SSSR, 281:5 (1985),  1061–1063
  66. Optimization of regularization methods in the solution of degenerate operator equations

    Izv. Vyssh. Uchebn. Zaved. Mat., 1985, no. 9,  75–76
  67. Finite-dimensional approximation of the regularization method in the solution of inverse problems

    Dokl. Akad. Nauk SSSR, 277:3 (1984),  557–559
  68. Necessary and sufficient conditions for convergence of approximations of linear ill-posed problems in a Hilbert space

    Zh. Vychisl. Mat. Mat. Fiz., 24:5 (1984),  633–639
  69. On order-optimal regularization of linear operator equations under the condition of nonuniqueness of solutions

    Dokl. Akad. Nauk SSSR, 269:1 (1983),  37–38
  70. Necessary and sufficient conditions for convergence of finite-dimensional approximations of regularized solutions

    Dokl. Akad. Nauk SSSR, 264:5 (1982),  1094–1096
  71. Selection of the regularization parameter in the solution of ill-posed problems

    Sibirsk. Mat. Zh., 21:4 (1980),  161–168
  72. On the solution of implicit operator equations of the first kind and their applications

    Dokl. Akad. Nauk SSSR, 244:5 (1979),  1085–1087
  73. The principle of minimal residuals

    Dokl. Akad. Nauk SSSR, 239:4 (1978),  800–803
  74. Approximate solution of implicit operator equations of the first kind by the regularization method

    Izv. Vyssh. Uchebn. Zaved. Mat., 1978, no. 11,  98–103
  75. Determination of the energy spectrum of a Bose system by thermodynamic functions

    Zh. Vychisl. Mat. Mat. Fiz., 18:6 (1978),  1500–1515
  76. The realization of the method of quasisolutions

    Izv. Vyssh. Uchebn. Zaved. Mat., 1977, no. 12,  108–113
  77. The classification of ill-posed problems and optimal methods for their solution

    Izv. Vyssh. Uchebn. Zaved. Mat., 1977, no. 11,  106–112
  78. The $\beta$-convergence of the projection method for operator equations of the first kind with a nonlinear operator

    Izv. Vyssh. Uchebn. Zaved. Mat., 1977, no. 8,  79–83
  79. The solution of operator equations of the first kind with multivalued operators, and their application

    Izv. Vyssh. Uchebn. Zaved. Mat., 1977, no. 7,  87–93
  80. On optimal algorithms for operator equations of the first kind with a perturbed operator

    Mat. Sb. (N.S.), 104(146):2(10) (1977),  314–333
  81. On optimal methods for solving illposed problems with an approximately specified operator and error estimates for the methods

    Zh. Vychisl. Mat. Mat. Fiz., 17:2 (1977),  291–297
  82. A projective-iterative algorithm for the solution of ill-posed problems with an approximately given operator

    Zh. Vychisl. Mat. Mat. Fiz., 17:1 (1977),  15–23
  83. Determination of the phonon density of the states from thermodynamic functions of the crystal

    Dokl. Akad. Nauk SSSR, 231:4 (1976),  845–848
  84. On projection methods for solving nonlinear unstable problems

    Dokl. Akad. Nauk SSSR, 229:3 (1976),  558–561
  85. The possibility of determining the energy spectrum of a Bose system from thermodynamic functions

    Dokl. Akad. Nauk SSSR, 228:1 (1976),  19–22
  86. On an optimal algorithm for operator equations of the first kind with a perturbed operator

    Dokl. Akad. Nauk SSSR, 226:6 (1976),  1279–1282
  87. The optimality of regularizing algorithms in the solution of ill-posed problems

    Differ. Uravn., 12:7 (1976),  1323–1326
  88. Elements of approximation theory in locally convex topological spaces

    Izv. Vyssh. Uchebn. Zaved. Mat., 1976, no. 6,  73–76
  89. Optimal algorithms for the solution of nonlinear unstable problems

    Sibirsk. Mat. Zh., 17:5 (1976),  1116–1128
  90. Order-optimal methods for the solution of nonlinear ill-posed problems

    Zh. Vychisl. Mat. Mat. Fiz., 16:2 (1976),  503–507
  91. On a projection-iterative algorithm for operator equations of the first kind with a perturbed operator

    Dokl. Akad. Nauk SSSR, 224:5 (1975),  1028–1029
  92. On the optimality of methods of solving nonlinear unstable problems

    Dokl. Akad. Nauk SSSR, 220:5 (1975),  1035–1037
  93. Projection-iteration methods for the solution of operator equations of the first kind

    Izv. Vyssh. Uchebn. Zaved. Mat., 1975, no. 5,  73–77
  94. Projection methods and finite-difference approximation of linear incorrectly formulated problems

    Sibirsk. Mat. Zh., 16:6 (1975),  1301–1307
  95. The stability of projection methods in the solution of ill-posed problems

    Zh. Vychisl. Mat. Mat. Fiz., 15:1 (1975),  19–29
  96. Necessary and sufficient conditions for convergence of projection methods for linear unstable problems

    Dokl. Akad. Nauk SSSR, 215:5 (1974),  1032–1034
  97. The stability of the method of the residual in the solution of ill-posed problems

    Izv. Vyssh. Uchebn. Zaved. Mat., 1974, no. 9,  75–80
  98. Approximate solution of operator equations of the first kind in locally convex spaces

    Izv. Vyssh. Uchebn. Zaved. Mat., 1973, no. 9,  70–77
  99. Approximate solution of operator equations of the first kind and the geometric properties of Banach spaces

    Izv. Vyssh. Uchebn. Zaved. Mat., 1971, no. 7,  81–93
  100. Ill-posed problems and geometries of Banach spaces

    Dokl. Akad. Nauk SSSR, 193:1 (1970),  43–45

  101. On optimal methods of solution to linear equations of the first kind with an approximately specified operator

    Sib. Zh. Vychisl. Mat., 6:2 (2003),  205–208
  102. Valentin Konstantinovich Ivanov (on the occasion of his eightieth birthday)

    Izv. Vyssh. Uchebn. Zaved. Mat., 1988, no. 10,  3–4

© Steklov Math. Inst. of RAS, 2024