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Leonov Aleksandr Sergeevich

Publications in Math-Net.Ru

  1. A structural two-level neural network approach to joint inversion of gravitational and magnetic fields

    Num. Meth. Prog., 26:3 (2025),  322–339
  2. Methods for solving ill-conditioned systems of linear algebraic equations that improve the conditionality

    Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 8,  34–44
  3. "Fast" algorithm for solving some three-dimensional inverse problems of magnetometry

    Mat. Model., 36:1 (2024),  41–58
  4. Solving some inverse problems of gravimetry and magnetometry using an algorithm that improves matrix conditioning

    Zh. Vychisl. Mat. Mat. Fiz., 64:10 (2024),  1795–1808
  5. “Fast” solution of the three-dimensional inverse problem of quasi-static elastography with the help of the small parameter method

    Zh. Vychisl. Mat. Mat. Fiz., 63:3 (2023),  449–464
  6. Computing magnifier for refining the position and shape of three-dimensional objects in acoustic sensing

    Mat. Model., 34:5 (2022),  3–26
  7. Solution of the two-dimensional inverse problem of quasistatic elastography with the help of the small parameter method

    Zh. Vychisl. Mat. Mat. Fiz., 62:5 (2022),  854–860
  8. Fast solution algorithm for a three-dimensional inverse multifrequency problem of scalar acoustics with data in a cylindrical domain

    Zh. Vychisl. Mat. Mat. Fiz., 62:2 (2022),  289–304
  9. Effective algorithms for computing global and local posterior error estimates of solutions to linear ill-posed problems

    Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 2,  29–38
  10. On phase correction in tomographic research

    Sib. Zh. Ind. Mat., 23:4 (2020),  18–29
  11. Numerical solution of an inverse multifrequency problem in scalar acoustics

    Zh. Vychisl. Mat. Mat. Fiz., 60:6 (2020),  1013–1026
  12. Extra-optimal methods for solving ill-posed problems: survey of theory and examples

    Zh. Vychisl. Mat. Mat. Fiz., 60:6 (2020),  985–1012
  13. Methods for solving ill-posed extremum problems with optimal and extra-optimal quality

    Mat. Zametki, 105:3 (2019),  406–420
  14. Numerical solution to a three-dimensional coefficient inverse problem for the wave equation with integral data in a cylindrical domain

    Sib. Zh. Vychisl. Mat., 22:4 (2019),  381–397
  15. A new algorithm for a posteriori error estimation for approximate solutions of linear ill-posed problems

    Zh. Vychisl. Mat. Mat. Fiz., 59:2 (2019),  203–210
  16. Low-cost numerical method for solving a coefficient inverse problem for the wave equation in three-dimensional space

    Zh. Vychisl. Mat. Mat. Fiz., 58:4 (2018),  561–574
  17. On possibility of obtaining linear accuracy evaluation of approximate solutions to inverse problems

    Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 10,  29–35
  18. Regularizing algorithms with optimal and extra-optimal quality

    Sib. Zh. Vychisl. Mat., 19:4 (2016),  371–383
  19. Locally extra-optimal regularizing algorithms and a posteriori estimates of the accuracy for ill-posed problems with discontinuous solutions

    Zh. Vychisl. Mat. Mat. Fiz., 56:1 (2016),  3–15
  20. Which of inverse problems can have a priori approximate solution accuracy estimates comparable in order with the data accuracy

    Sib. Zh. Vychisl. Mat., 17:4 (2014),  339–348
  21. New a posteriori error estimates for approximate solutions to iregular operator equations

    Num. Meth. Prog., 15:2 (2014),  359–369
  22. Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?

    Zh. Vychisl. Mat. Mat. Fiz., 54:4 (2014),  562–568
  23. Pointwise extra-optimal regularizing algorithms

    Num. Meth. Prog., 14:2 (2013),  215–228
  24. A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution

    Sib. Zh. Vychisl. Mat., 15:1 (2012),  83–100
  25. Higher-order total variations for functions of several variables and their application in the theory of ill-posed problems

    Trudy Inst. Mat. i Mekh. UrO RAN, 18:1 (2012),  198–212
  26. On a posteriori accuracy estimates for solutions of linear ill-posed problems and extra-optimal regularizing algorithms

    Num. Meth. Prog., 11:1 (2010),  14–24
  27. On elimination of accuracy saturation of regularizing algorithms

    Sib. Zh. Vychisl. Mat., 11:2 (2008),  167–186
  28. On the total-variation convergence of regularizing algorithms for ill-posed problems

    Zh. Vychisl. Mat. Mat. Fiz., 47:5 (2007),  767–783
  29. On the $H$-property of functionals in Sobolev spaces

    Mat. Zametki, 77:3 (2005),  378–394
  30. Functionals with the $H$-property in the Sobolev space $W_1^1$

    Mat. Sb., 195:6 (2004),  121–136
  31. General regularizing functionals for solving ill-posed problems in Lebesgue spaces

    Sibirsk. Mat. Zh., 44:6 (2003),  1295–1309
  32. Numerical implementation of special regularizing algorithms for solving a class of ill-posed problems with sourcewise represented solutions

    Sib. Zh. Vychisl. Mat., 4:3 (2001),  269–280
  33. Adaptive optimal algorithms for ill-posed problems with sourcewise represented solutions

    Zh. Vychisl. Mat. Mat. Fiz., 41:6 (2001),  855–873
  34. A generalization of the maximal entropy method for solving ill-posed problems

    Sibirsk. Mat. Zh., 41:4 (2000),  863–872
  35. Application of function of several variables with bounded variation to numerical solution of two-dimensional ill-posed problems

    Sib. Zh. Vychisl. Mat., 2:3 (1999),  257–271
  36. Piecewise uniform regularization of two-dimensional ill-posed problems with discontinuous solutions

    Zh. Vychisl. Mat. Mat. Fiz., 39:12 (1999),  1939–1944
  37. Optimal methods for solving ill-posed problems with sourcewise representated solutions

    Fundam. Prikl. Mat., 4:3 (1998),  1029–1046
  38. On the total variation for functions of several variables and a multidimensional analog of Helly's selection principle

    Mat. Zametki, 63:1 (1998),  69–80
  39. On multidimensional ill-posed problems with discontinuous solutions

    Sibirsk. Mat. Zh., 39:1 (1998),  74–86
  40. Some remarks on the minimal pseudoinverse matrix method

    Zh. Vychisl. Mat. Mat. Fiz., 38:7 (1998),  1085–1090
  41. On the use of functions of several variables with bounded variation for piecewise-uniform regularization of ill-posed problems

    Dokl. Akad. Nauk, 351:5 (1996),  592–595
  42. Functions of several variables with bounded variation in ill-posed problems

    Zh. Vychisl. Mat. Mat. Fiz., 36:9 (1996),  35–49
  43. Pseudo-optimal choice of parameter in the regularization method

    Zh. Vychisl. Mat. Mat. Fiz., 35:7 (1995),  1034–1049
  44. Some a posteriori termination rules for the iterative solution of linear ill-posed problems

    Zh. Vychisl. Mat. Mat. Fiz., 34:1 (1994),  148–154
  45. On quasioptimum selection of the regularization parameter in M. M. Lavrent'ev's method

    Sibirsk. Mat. Zh., 34:4 (1993),  117–126
  46. On the accuracy of Tikhonov regularizing algorithms and the quasi-optimal choice of regularization parameter

    Dokl. Akad. Nauk SSSR, 321:3 (1991),  460–465
  47. Problem of precision of the method of a minimal pseudoinverse matrix

    Mat. Zametki, 49:4 (1991),  81–87
  48. The minimum pseudo-inverse matrix method: Theory and numerical implementation

    Zh. Vychisl. Mat. Mat. Fiz., 31:10 (1991),  1427–1443
  49. On the theory of the method of the minimal pseudo-inverse matrix

    Dokl. Akad. Nauk SSSR, 314:1 (1990),  89–93
  50. Order optimality of the accuracy of some algorithms for solving ill-posed extremal problems

    Izv. Vyssh. Uchebn. Zaved. Mat., 1990, no. 6,  30–38
  51. Optimality with respect to the order of accuracy of the generalized principle of the residual and of some other algorithms for the solution of nonlinear ill-posed problems with approximate data

    Sibirsk. Mat. Zh., 29:6 (1988),  85–94
  52. Numerical realization of piecewise-uniform regularization algorithms

    Zh. Vychisl. Mat. Mat. Fiz., 27:9 (1987),  1412–1416
  53. The minimal pseudo-inverse matrix method

    Zh. Vychisl. Mat. Mat. Fiz., 27:8 (1987),  1123–1138
  54. On determining the optimal conditions of introducing an antibacterial drug

    Avtomat. i Telemekh., 1986, no. 1,  100–106
  55. On the optimal mathematical design of electromagnet systems

    Dokl. Akad. Nauk SSSR, 287:2 (1986),  312–316
  56. On some algorithms for solving ill-posed extremal problems

    Mat. Sb. (N.S.), 129(171):2 (1986),  218–231
  57. The method of a minimal pseudoinverse matrix for solving ill-posed problems of linear algebra

    Dokl. Akad. Nauk SSSR, 285:1 (1985),  36–40
  58. Approximate calculation of a pseudoinverse matrix using a generalized discrepancy principle

    Zh. Vychisl. Mat. Mat. Fiz., 25:6 (1985),  933–935
  59. On the solution of linear ill-posed problems on the basis of a modified quasioptimality criterion

    Mat. Sb. (N.S.), 122(164):3(11) (1983),  405–415
  60. On an application of the generalized residual principle for the solution of ill-posed extremal problems

    Dokl. Akad. Nauk SSSR, 262:6 (1982),  1306–1310
  61. On choosing a regularization parameter by means of the quasi-optimality and ratio criteria for ill-posed linear algebra problems with a perturbed operator

    Dokl. Akad. Nauk SSSR, 262:5 (1982),  1069–1072
  62. The connection between the generalized residual method and the generalized principle of the residual for nonlinear ill-posed problems

    Zh. Vychisl. Mat. Mat. Fiz., 22:4 (1982),  783–790
  63. Piecewise-uniform regularization of ill-posed problems with discontinuous solutions

    Zh. Vychisl. Mat. Mat. Fiz., 22:3 (1982),  516–531
  64. On the regularization of ill-posed problems with discontinuous solutions and an application of this methodology for the solution of some nonlinear equations

    Dokl. Akad. Nauk SSSR, 250:1 (1980),  31–35
  65. On functions of bounded generalized variation

    Dokl. Akad. Nauk SSSR, 249:4 (1979),  787–789
  66. On algorithms for an approximate solution of nonlinear ill-posed problems with a perturbed operator

    Dokl. Akad. Nauk SSSR, 245:2 (1979),  300–304
  67. Choice of regularization parameter for non-linear ill-posed problems with approximately specified operator

    Zh. Vychisl. Mat. Mat. Fiz., 19:6 (1979),  1363–1376
  68. On the choice of regularization parameters by means of the quasi- optimality and ratio criteria

    Dokl. Akad. Nauk SSSR, 240:1 (1978),  18–20
  69. On the justification of the choice of the regularization parameter based on quasi-optimality and relation tests

    Zh. Vychisl. Mat. Mat. Fiz., 18:6 (1978),  1363–1376
  70. Calculation of the values of unbounded operators by the averaging method

    Dokl. Akad. Nauk SSSR, 235:1 (1977),  23–26
  71. On the construction of stable difference schemes for solving nonlinear boundary value problems

    Dokl. Akad. Nauk SSSR, 224:3 (1975),  525–528
  72. The construction of stable difference schemes for second order linear differential operators of indefinite sign

    Zh. Vychisl. Mat. Mat. Fiz., 15:3 (1975),  635–643
  73. The applicability of the principle of the residual in the case of nonlinear ill-posed problems, and a new regularizing algorithm for their solution

    Zh. Vychisl. Mat. Mat. Fiz., 15:2 (1975),  290–297
  74. On the residual principle for solving nonlinear ill-posed problems

    Dokl. Akad. Nauk SSSR, 214:3 (1974),  499–500
  75. The regularization of ill-posed problems with approximately given operator

    Zh. Vychisl. Mat. Mat. Fiz., 14:4 (1974),  1022–1027
  76. Finite difference approximation of linear ill-posed problems

    Zh. Vychisl. Mat. Mat. Fiz., 14:1 (1974),  15–24
  77. A generalized residual principle

    Zh. Vychisl. Mat. Mat. Fiz., 13:2 (1973),  294–302
  78. A generalization of the discrepancy principle for the case of an operator specified with an error

    Dokl. Akad. Nauk SSSR, 203:6 (1972),  1238–1239
  79. A certain regularizing algorithm for ill-posed problems with an approximately given operator

    Zh. Vychisl. Mat. Mat. Fiz., 12:6 (1972),  1592–1594
  80. Certain estimates of the rate of convergence of regularized approximations for equations of convolution type

    Zh. Vychisl. Mat. Mat. Fiz., 12:3 (1972),  762–770
  81. Certain algorithms for finding the approximate solution of ill-posed problems on a set of monotone functions

    Zh. Vychisl. Mat. Mat. Fiz., 12:2 (1972),  283–297
  82. The solution of two-dimensional Fredholm integral equations of the first kind with a kernel that depends on the difference of the arguments

    Zh. Vychisl. Mat. Mat. Fiz., 11:5 (1971),  1296–1301

  83. Inverse problems in partial differential equations. Eds D. Colton, R. Ewing, W. Rundell. Proc. SIAM. Philadelphia, 1990. Book review

    Zh. Vychisl. Mat. Mat. Fiz., 32:7 (1992),  1149–1150

© Steklov Math. Inst. of RAS, 2026