ill-posed problems; first kind equations; regularization; convergence domain; error estimates; approximation of functions.
Biography
Graduated from Faculty of Mathematics and Mechanics of Saratov State University in 1958. Ph.D. thesis was defended in 1973. D.Sci. thesis was defended in 1999. A list of my works contains more than titles.
Main publications:
Khromova G. V. Priblizhayuschie svoistva rezolvent differentsialnykh operatorov v zadache priblizheniya funktsii i ikh proizvodnykh // Zhurn. vychislit. matematiki i matem. fiziki, 1998, t. 38, # 7, 1106–1113.
Khromova G. V. Ob obratnoi zadache dlya obyknovennogo differentsialnogo uravneniya // Fundam. i prikladnaya matematika, 1998, t. 4, vyp. 2, 709–716.
Khromova G. V. Ob odnom sposobe postroeniya metodov regulyarizatsii uravnenii pervogo roda // Zhurn. vychisl. matematiki i matem. fiziki, 2000, t. 40, # 7, 907–1102.
Khromova G. V. Ob otsenkakh pogreshnosti priblizhennykh reshenii uravnenii pervogo roda // Doklady RAN, 2001, t. 378, # 5, 1–5.
G. V. Khromova, “Operators with discontinuous range and their applications”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 200 (2021), 58–64
2018
2.
G. V. Khromova, “Regularization of the Abel integral equation with perturbation”, Zh. Vychisl. Mat. Mat. Fiz., 58:6 (2018), 945–950; Comput. Math. Math. Phys., 58:6 (2018), 909–914
2016
3.
G. V. Khromova, “On operators with discontinuous range”, Izv. Saratov Univ. Math. Mech. Inform., 16:3 (2016), 298–302
2015
4.
A. A. Khromov, G. V. Khromova, “The solution of the problem of determining the density of heat sources in a rod”, Izv. Saratov Univ. Math. Mech. Inform., 15:3 (2015), 309–314
G. V. Khromova, “On uniform approximations to the solution of the Abel integral equation”, Zh. Vychisl. Mat. Mat. Fiz., 55:10 (2015), 1703–1712; Comput. Math. Math. Phys., 55:10 (2015), 1674–1683
G. V. Khromova, “Regularization of Abel Equation with the Use of Discontinuous Steklov Operator”, Izv. Saratov Univ. Math. Mech. Inform., 14:4(2) (2014), 599–603
A. P. Khromov, G. V. Khromova, “Discontinuous Steklov operators in the problem of uniform approximation of derivatives on an interval”, Zh. Vychisl. Mat. Mat. Fiz., 54:9 (2014), 1442–1557; Comput. Math. Math. Phys., 54:9 (2014), 1389–1394
A. P. Khromov, G. V. Khromova, “A family of operators with discontinuous ranges and approximation and restoration of continuous functions”, Zh. Vychisl. Mat. Mat. Fiz., 53:10 (2013), 1603–1609; Comput. Math. Math. Phys., 53:10 (2013), 1421–1427
A. P. Khromov, G. V. Khromova, “On the convergence of the Lavrent'ev method for an integral equation of the first kind with involution”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:1 (2012), 289–297; Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 88–97
A. P. Khromov, G. V. Khromova, “On the regularization of a class of integral equations of the first kind whose kernels are discontinuous on the diagonals”, Zh. Vychisl. Mat. Mat. Fiz., 52:8 (2012), 1363–1372; Comput. Math. Math. Phys., 52:8 (2012), 1079–1088
2011
11.
A. A. Khromov, G. V. Khromova, “Approximating properties of solutions of the differential equation with integral boundary condition”, Izv. Saratov Univ. Math. Mech. Inform., 11:3(2) (2011), 63–66
12.
A. A. Khromov, G. V. Khromova, “On the construction of approximations to continuous functions under integral boundary conditions”, Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011), 1370–1375; Comput. Math. Math. Phys., 51:8 (2011), 1280–1285
2009
13.
G. V. Khromova, “Convergence of the Lavrent'ev method”, Zh. Vychisl. Mat. Mat. Fiz., 49:6 (2009), 958–965; Comput. Math. Math. Phys., 49:6 (2009), 919–926
A. A. Khromov, G. V. Khromova, “Finding approximations of continuous solutions to first-kind equations”, Zh. Vychisl. Mat. Mat. Fiz., 49:2 (2009), 225–231; Comput. Math. Math. Phys., 49:2 (2009), 217–223
S. Yu. Sovetnikova, G. V. Khromova, “On the regularization of an equation of the first kind with a multiple integration operator”, Zh. Vychisl. Mat. Mat. Fiz., 47:4 (2007), 578–586; Comput. Math. Math. Phys., 47:4 (2007), 555–563
2006
16.
G. V. Khromova, “On the moduli of continuity of unbounded operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2006, no. 9, 71–78; Russian Math. (Iz. VUZ), 50:9 (2006), 67–74
G. V. Khromova, E. V. Shishkova, “Constructing regularization methods in the spaces of differentiable functions”, Zh. Vychisl. Mat. Mat. Fiz., 46:11 (2006), 1915–1922; Comput. Math. Math. Phys., 46:11 (2006), 1827–1834
2005
18.
G. V. Khromova, “On the regularization of a class of integral equations of the first kind”, Zh. Vychisl. Mat. Mat. Fiz., 45:10 (2005), 1810–1817; Comput. Math. Math. Phys., 45:10 (2005), 1743–1750
A. P. Khromov, G. V. Khromova, “Extension of the convergence domain in the Tikhonov method”, Zh. Vychisl. Mat. Mat. Fiz., 42:8 (2002), 1109–1114; Comput. Math. Math. Phys., 42:8 (2002), 1067–1072
G. V. Khromova, “A method for constructing regularization techniques for equations of the first kind”, Zh. Vychisl. Mat. Mat. Fiz., 40:7 (2000), 997–1002; Comput. Math. Math. Phys., 40:7 (2000), 955–960
G. V. Khromova, “Approximating properties of resolvents of differential operators in the approximation problem for functions and their derivatives”, Zh. Vychisl. Mat. Mat. Fiz., 38:7 (1998), 1106–1113; Comput. Math. Math. Phys., 38:7 (1998), 1057–1064
G. V. Khromova, “The problem of the reconstruction of functions that are given with error”, Zh. Vychisl. Mat. Mat. Fiz., 17:5 (1977), 1161–1171; U.S.S.R. Comput. Math. Math. Phys., 17:5 (1977), 58–68
G. V. Khromova, “The regularization of integral equations of the first kind with a Green's kernel”, Izv. Vyssh. Uchebn. Zaved. Mat., 1972, no. 8, 94–104
G. V. Khromova, “Correction to: “On a technique for constructing regularization methods for equations of the first kind””, Zh. Vychisl. Mat. Mat. Fiz., 40:10 (2000), 1584
Presentations in Math-Net.Ru
1.
Разрывный оператор Стеклова и полиномиальные сплайны G. V. Khromova XXII International Saratov Winter School
"Contemporary Problems of Function Theory and Their Applications",
dedicated to the 300th anniversary of the Russian Academy of Sciences January 28, 2024 16:00
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