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Leonov, Aleksandr Sergeevich
Statistics Math-Net.Ru
Total publications: 81
Scientific articles: 80

Number of views:
This page:5156
Abstract pages:22185
Full texts:8540
References:1734
Professor
Doctor of physico-mathematical sciences
E-mail: , , ,

https://www.mathnet.ru/eng/person14357
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/196346

Publications in Math-Net.Ru Citations
2024
1. A. S. Leonov, “Methods for solving ill-conditioned systems of linear algebraic equations that improve the conditionality”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 8,  34–44  mathnet
2. A. S. Leonov, D. V. Lukyanenko, A. G. Yagola, “"Fast" algorithm for solving some three-dimensional inverse problems of magnetometry”, Matem. Mod., 36:1 (2024),  41–58  mathnet
2023
3. A. S. Leonov, N. N. Nefedov, A. N. Sharov, A. G. Yagola, ““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  mathnet  elib; Comput. Math. Math. Phys., 63:3 (2023), 425–440 1
2022
4. A. B. Bakushinsky, A. S. Leonov, “Computing magnifier for refining the position and shape of three-dimensional objects in acoustic sensing”, Matem. Mod., 34:5 (2022),  3–26  mathnet  mathscinet
5. A. S. Leonov, N. N. Nefedov, A. N. Sharov, A. G. Yagola, “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  mathnet  elib; Comput. Math. Math. Phys., 62:5 (2022), 827–833  scopus 1
6. A. B. Bakushinskii, A. S. Leonov, “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  mathnet  elib; Comput. Math. Math. Phys., 62:2 (2022), 287–301  isi  scopus 6
2020
7. A. S. Leonov, “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  mathnet; Russian Math. (Iz. VUZ), 64:2 (2020), 26–34  isi  scopus 6
8. Ya. Wang, A. S. Leonov, D. V. Lukyanenko, V. D. Shinkarev, A. G. Yagola, “On phase correction in tomographic research”, Sib. Zh. Ind. Mat., 23:4 (2020),  18–29  mathnet  elib; J. Appl. Industr. Math., 14:4 (2020), 802–810  scopus 3
9. A. B. Bakushinskii, A. S. Leonov, “Numerical solution of an inverse multifrequency problem in scalar acoustics”, Zh. Vychisl. Mat. Mat. Fiz., 60:6 (2020),  1013–1026  mathnet  elib; Comput. Math. Math. Phys., 60:6 (2020), 987–999  isi  scopus 8
10. A. S. Leonov, “Extra-optimal methods for solving ill-posed problems: survey of theory and examples”, Zh. Vychisl. Mat. Mat. Fiz., 60:6 (2020),  985–1012  mathnet  elib; Comput. Math. Math. Phys., 60:6 (2020), 960–986  isi  scopus 3
2019
11. A. S. Leonov, “Methods for solving ill-posed extremum problems with optimal and extra-optimal quality”, Mat. Zametki, 105:3 (2019),  406–420  mathnet  mathscinet  elib; Math. Notes, 105:3 (2019), 385–397  isi  scopus 2
12. A. B. Bakushinsky, A. S. Leonov, “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  mathnet; Num. Anal. Appl., 12:4 (2019), 311–325  isi 1
13. A. S. Leonov, “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  mathnet  elib; Comput. Math. Math. Phys., 59:2 (2019), 193–200  isi  scopus 1
2018
14. A. B. Bakushinskii, A. S. Leonov, “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  mathnet  elib; Comput. Math. Math. Phys., 58:4 (2018), 548–561  isi  scopus 13
2016
15. A. S. Leonov, “On possibility of obtaining linear accuracy evaluation of approximate solutions to inverse problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 10,  29–35  mathnet; Russian Math. (Iz. VUZ), 60:10 (2016), 23–28  isi  scopus 5
16. A. S. Leonov, “Regularizing algorithms with optimal and extra-optimal quality”, Sib. Zh. Vychisl. Mat., 19:4 (2016),  371–383  mathnet  mathscinet  elib; Num. Anal. Appl., 9:4 (2016), 288–298  isi  scopus 2
17. A. S. Leonov, “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  mathnet  elib; Comput. Math. Math. Phys., 56:1 (2016), 1–13  isi  scopus 4
2014
18. A. S. Leonov, “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  mathnet  mathscinet; Num. Anal. Appl., 7:4 (2014), 284–292 6
19. A. B. Bakushinskii, A. S. Leonov, “New a posteriori error estimates for approximate solutions to iregular operator equations”, Num. Meth. Prog., 15:2 (2014),  359–369  mathnet 4
20. A. S. Leonov, “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  mathnet  elib; Comput. Math. Math. Phys., 54:4 (2014), 575–581  isi  elib  scopus 7
2013
21. A. S. Leonov, “Pointwise extra-optimal regularizing algorithms”, Num. Meth. Prog., 14:2 (2013),  215–228  mathnet 3
2012
22. A. S. Leonov, “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  mathnet  elib; Num. Anal. Appl., 5:1 (2012), 68–83  scopus 25
23. A. S. Leonov, “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  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 119–133  isi  scopus 2
2010
24. A. S. Leonov, “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  mathnet 7
2008
25. A. S. Leonov, “On elimination of accuracy saturation of regularizing algorithms”, Sib. Zh. Vychisl. Mat., 11:2 (2008),  167–186  mathnet; Num. Anal. Appl., 1:2 (2008), 135–150 6
2007
26. A. S. Leonov, “On the total-variation convergence of regularizing algorithms for ill-posed problems”, Zh. Vychisl. Mat. Mat. Fiz., 47:5 (2007),  767–783  mathnet  mathscinet  elib; Comput. Math. Math. Phys., 47:5 (2007), 732–747  elib  scopus 7
2005
27. A. S. Leonov, “On the $H$-property of functionals in Sobolev spaces”, Mat. Zametki, 77:3 (2005),  378–394  mathnet  mathscinet  zmath; Math. Notes, 77:3 (2005), 348–363  isi  scopus 3
2004
28. A. S. Leonov, “Functionals with the $H$-property in the Sobolev space $W_1^1$”, Mat. Sb., 195:6 (2004),  121–136  mathnet  mathscinet  zmath; Sb. Math., 195:6 (2004), 879–896  isi  scopus 2
2003
29. A. S. Leonov, “General regularizing functionals for solving ill-posed problems in Lebesgue spaces”, Sibirsk. Mat. Zh., 44:6 (2003),  1295–1309  mathnet  mathscinet  zmath; Siberian Math. J., 44:6 (2003), 1015–1026q  isi 3
2001
30. A. S. Leonov, “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  mathnet  zmath 4
31. A. S. Leonov, A. G. Yagola, “Adaptive optimal algorithms for ill-posed problems with sourcewise represented solutions”, Zh. Vychisl. Mat. Mat. Fiz., 41:6 (2001),  855–873  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 41:6 (2001), 807–824 2
2000
32. A. S. Leonov, “A generalization of the maximal entropy method for solving ill-posed problems”, Sibirsk. Mat. Zh., 41:4 (2000),  863–872  mathnet  mathscinet  zmath; Siberian Math. J., 41:4 (2000), 716–724  isi 9
1999
33. A. S. Leonov, “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  mathnet  zmath 5
34. A. S. Leonov, “Piecewise uniform regularization of two-dimensional ill-posed problems with discontinuous solutions”, Zh. Vychisl. Mat. Mat. Fiz., 39:12 (1999),  1939–1944  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 39:12 (1999), 1861–1866 8
1998
35. A. S. Leonov, A. G. Yagola, “Optimal methods for solving ill-posed problems with sourcewise representated solutions”, Fundam. Prikl. Mat., 4:3 (1998),  1029–1046  mathnet  mathscinet  zmath
36. A. S. Leonov, “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  mathnet  mathscinet  zmath; Math. Notes, 63:1 (1998), 61–71  isi 27
37. A. S. Leonov, “On multidimensional ill-posed problems with discontinuous solutions”, Sibirsk. Mat. Zh., 39:1 (1998),  74–86  mathnet  mathscinet  zmath; Siberian Math. J., 39:1 (1998), 63–73  isi 4
38. A. S. Leonov, “Some remarks on the minimal pseudoinverse matrix method”, Zh. Vychisl. Mat. Mat. Fiz., 38:7 (1998),  1085–1090  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 38:7 (1998), 1036–1041
1996
39. A. S. Leonov, “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  mathnet  mathscinet  zmath 5
40. A. S. Leonov, “Functions of several variables with bounded variation in ill-posed problems”, Zh. Vychisl. Mat. Mat. Fiz., 36:9 (1996),  35–49  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 36:9 (1996), 1193–1203  isi 11
1995
41. A. S. Leonov, “Pseudo-optimal choice of parameter in the regularization method”, Zh. Vychisl. Mat. Mat. Fiz., 35:7 (1995),  1034–1049  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 35:7 (1995), 825–836  isi 3
1994
42. A. S. Leonov, “Some a posteriori termination rules for the iterative solution of linear ill-posed problems”, Zh. Vychisl. Mat. Mat. Fiz., 34:1 (1994),  148–154  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 34:1 (1994), 121–126  isi 1
1993
43. A. S. Leonov, “On quasioptimum selection of the regularization parameter in M. M. Lavrent'ev's method”, Sibirsk. Mat. Zh., 34:4 (1993),  117–126  mathnet  mathscinet  zmath; Siberian Math. J., 34:4 (1993), 695–703  isi 7
1991
44. A. S. Leonov, “On the accuracy of Tikhonov regularizing algorithms and the quasi-optimal choice of regularization parameter”, Dokl. Akad. Nauk SSSR, 321:3 (1991),  460–465  mathnet  mathscinet  zmath; Dokl. Math., 44:3 (1992), 711–716 1
45. A. S. Leonov, “Problem of precision of the method of a minimal pseudoinverse matrix”, Mat. Zametki, 49:4 (1991),  81–87  mathnet  mathscinet  zmath; Math. Notes, 49:4 (1991), 386–390  isi
46. A. S. Leonov, “The minimum pseudo-inverse matrix method: Theory and numerical implementation”, Zh. Vychisl. Mat. Mat. Fiz., 31:10 (1991),  1427–1443  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 31:10 (1991), 1–13  isi 1
1990
47. A. S. Leonov, “On the theory of the method of the minimal pseudo-inverse matrix”, Dokl. Akad. Nauk SSSR, 314:1 (1990),  89–93  mathnet  mathscinet  zmath; Dokl. Math., 42:2 (1991), 327–332 1
48. A. S. Leonov, “Order optimality of the accuracy of some algorithms for solving ill-posed extremal problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1990, no. 6,  30–38  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 34:6 (1990), 35–44
1988
49. A. S. Leonov, “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  mathnet  mathscinet  zmath; Siberian Math. J., 29:6 (1988), 940–947  isi 2
1987
50. A. S. Leonov, “Numerical realization of piecewise-uniform regularization algorithms”, Zh. Vychisl. Mat. Mat. Fiz., 27:9 (1987),  1412–1416  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 27:5 (1987), 88–91 3
51. A. S. Leonov, “The minimal pseudo-inverse matrix method”, Zh. Vychisl. Mat. Mat. Fiz., 27:8 (1987),  1123–1138  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 27:4 (1987), 107–117 4
1986
52. A. L. Korotaev, P. I. Kuznetsov, A. S. Leonov, V. Y. Rodaman, “On determining the optimal conditions of introducing an antibacterial drug”, Avtomat. i Telemekh., 1986, no. 1,  100–106  mathnet
53. S. P. Krekoten, A. S. Leonov, V. G. Sukharevsky, “On the optimal mathematical design of electromagnet systems”, Dokl. Akad. Nauk SSSR, 287:2 (1986),  312–316  mathnet
54. A. S. Leonov, “On some algorithms for solving ill-posed extremal problems”, Mat. Sb. (N.S.), 129(171):2 (1986),  218–231  mathnet  mathscinet  zmath; Math. USSR-Sb., 57:1 (1987), 229–242 10
1985
55. A. S. Leonov, “The method of a minimal pseudoinverse matrix for solving ill-posed problems of linear algebra”, Dokl. Akad. Nauk SSSR, 285:1 (1985),  36–40  mathnet  mathscinet  zmath
56. A. S. Leonov, “Approximate calculation of a pseudoinverse matrix using a generalized discrepancy principle”, Zh. Vychisl. Mat. Mat. Fiz., 25:6 (1985),  933–935  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 25:3 (1985), 181–182 7
1983
57. A. S. Leonov, “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  mathnet  mathscinet  zmath; Math. USSR-Sb., 50:2 (1985), 387–397 2
1982
58. A. S. Leonov, “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  mathnet  mathscinet  zmath 3
59. A. S. Leonov, “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  mathnet  mathscinet  zmath 1
60. A. S. Leonov, “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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 22:4 (1982), 13–22 3
61. A. S. Leonov, “Piecewise-uniform regularization of ill-posed problems with discontinuous solutions”, Zh. Vychisl. Mat. Mat. Fiz., 22:3 (1982),  516–531  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 22:3 (1982), 20–36 15
1980
62. A. S. Leonov, “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  mathnet  mathscinet  zmath
1979
63. A. S. Leonov, “On functions of bounded generalized variation”, Dokl. Akad. Nauk SSSR, 249:4 (1979),  787–789  mathnet  mathscinet  zmath
64. A. S. Leonov, “On algorithms for an approximate solution of nonlinear ill-posed problems with a perturbed operator”, Dokl. Akad. Nauk SSSR, 245:2 (1979),  300–304  mathnet  mathscinet  zmath
65. A. S. Leonov, “Choice of regularization parameter for non-linear ill-posed problems with approximately specified operator”, Zh. Vychisl. Mat. Mat. Fiz., 19:6 (1979),  1363–1376  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 19:6 (1979), 1–15 6
1978
66. A. S. Leonov, “On the choice of regularization parameters by means of the quasi- optimality and ratio criteria”, Dokl. Akad. Nauk SSSR, 240:1 (1978),  18–20  mathnet  mathscinet  zmath
67. A. S. Leonov, “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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 18:6 (1978), 1–15 13
1977
68. A. S. Leonov, “Calculation of the values of unbounded operators by the averaging method”, Dokl. Akad. Nauk SSSR, 235:1 (1977),  23–26  mathnet  mathscinet  zmath
1975
69. A. S. Leonov, “On the construction of stable difference schemes for solving nonlinear boundary value problems”, Dokl. Akad. Nauk SSSR, 224:3 (1975),  525–528  mathnet  mathscinet  zmath
70. Yu. A. Eremin, A. S. Leonov, “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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 15:3 (1975), 86–94
71. A. V. Goncharsky, A. S. Leonov, A. G. Yagola, “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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 15:2 (1975), 8–16
1974
72. A. V. Goncharsky, A. S. Leonov, A. G. Yagola, “On the residual principle for solving nonlinear ill-posed problems”, Dokl. Akad. Nauk SSSR, 214:3 (1974),  499–500  mathnet  mathscinet  zmath
73. A. V. Goncharsky, A. S. Leonov, A. G. Yagola, “The regularization of ill-posed problems with approximately given operator”, Zh. Vychisl. Mat. Mat. Fiz., 14:4 (1974),  1022–1027  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 14:4 (1974), 195–201 3
74. A. V. Goncharsky, A. S. Leonov, A. G. Yagola, “Finite difference approximation of linear ill-posed problems”, Zh. Vychisl. Mat. Mat. Fiz., 14:1 (1974),  15–24  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 14:1 (1974), 14–23 4
1973
75. A. V. Goncharsky, A. S. Leonov, A. G. Yagola, “A generalized residual principle”, Zh. Vychisl. Mat. Mat. Fiz., 13:2 (1973),  294–302  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 13:2 (1973), 25–37 38
1972
76. A. V. Goncharsky, A. S. Leonov, A. G. Yagola, “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  mathnet  mathscinet  zmath 1
77. A. V. Goncharsky, A. S. Leonov, A. G. Yagola, “A certain regularizing algorithm for ill-posed problems with an approximately given operator”, Zh. Vychisl. Mat. Mat. Fiz., 12:6 (1972),  1592–1594  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 12:6 (1972), 286–290 9
78. A. V. Goncharsky, A. S. Leonov, A. G. Yagola, “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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 12:3 (1972), 243–254 2
79. A. V. Goncharskii, L. G. Gushchina, A. S. Leonov, A. G. Yagola, “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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 12:2 (1972), 1–18 1
1971
80. A. V. Goncharsky, A. G. Yagola, A. S. Leonov, “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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 11:5 (1971), 253–260 3
1992
81. Yu. A. Eremin, A. S. Leonov, A. I. Prilepko, “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  mathnet

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