Solodky Sergii G.
Publications
The main publication are
Pereverzev, Sergei V.; Solodky, Sergei G.; Volynets, Evgeny A. The balancing principle in solving semi-discrete inverse problems in Sobolev scales by Tikhonov method. Appl. Anal. 91 (2012), no. 3, 435–446.
Solodky, Sergei G.; Mosentsova, Ganna Unsaturable methods for solving severely ill-posed problems. Int. J. Comput. Sci. Math. 2 (2009), no. 3, 229–242.
Solodky, S. G.; Mosentsova, A. Morozov's discrepancy principle for the Tikhonov regularization of exponentially ill-posed problems. Comput. Methods Appl. Math. 8 (2008), no. 1, 86–98.
Solodky, S. G.; Lebedeva, E. V. On reduction of informational expenses in solving ill-posed problems with not exactly given input data. J. Inverse Ill-Posed Probl. 16 (2008), no. 2, 195–207
Lebedeva, E. V.; Solodkiĭ, S. G. On the approximation of finite-interval equations by piecewise-constant functions. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 48 (2008), no. 5, 731--745; translation in Comput. Math. Math. Phys. 48 (2008), no. 5, 693–706
Solodky, S. G.; Lebedeva, E. V. On reduction of informational expenses in solving ill-posed problems with not exactly given input data. J. Inverse Ill-Posed Probl. 16 (2008), no. 2, 195–207.
Solodkiĭ, S. G.; Lebedeva, E. V. On piecewise-constant discretization in the method of finite intervals. (Russian) Dokl. Akad. Nauk 416 (2007), no. 1, 36--39; translation in Dokl. Math. 76 (2007), no. 2, 786–789
Solodky, S. G.; Lebedeva, E. V. Error bounds of a fully discrete projection method for Symm's integral equation. Comput. Methods Appl. Math. 7 (2007), no. 3, 255–263.
Solodky, S. G. Economic discretization scheme for the nonstationary iterated Tikhonov method. J. Optim. Theory Appl. 132 (2007), no. 1, 21–39.
Solodky, Sergei G.; Lebedeva, Evgeniya V. Bounds of information expenses in constructing projection methods for solving ill-posed problems. Comput. Methods Appl. Math. 6 (2006), no. 1, 87–93.
Solodkiĭ, S. G. An algorithm for solving Fredholm equations with analytic coefficients. (Russian) Differ. Uravn. 41 (2005), no. 9, 1286--1290, 1296; translation in Differ. Equ. 41 (2005), no. 9, 1359–1363
Solodky, S. G. On a quasi-optimal regularized projection method for solving operator equations of the first kind. Inverse Problems 21 (2005), no. 4, 1473–1485.
Solodky, Sergei G. The optimal approximations for stationary iterated Tikhonov method. East J. Approx. 10 (2004), no. 1-2, 189–200.
Solodkiĭ, S. G. On a discretization scheme for the Landweber method. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 44 (2004), no. 3, 387--396; translation in Comput. Math. Math. Phys. 44 (2004), no. 3, 363–372
Solodkiĭ, S. G. Adaptive discretization of ill-posed problems. (Russian) Dokl. Akad. Nauk 382 (2002), no. 4, 460–462.
Solodky, S. G. The optimal approximations for solving linear ill-posed problems. J. Complexity 17 (2001), no. 1, 98–116.
Maaß, Peter; Pereverzev, Sergei V.; Ramlau, Ronny; Solodky, Sergei G. An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection. Numer. Math. 87 (2001), no. 3, 485–502.
Solodky, S. G. A generalized projection scheme for solving ill-posed problems. J. Inverse Ill-Posed Probl. 7 (1999), no. 2, 185–200.
Solodky, S. G. Complexity for some classes of equations of the second kind. Facta Univ. Ser. Math. Inform. No. 14 (1999), 159–169.
Pereverzev, Sergei V.; Schock, Eberhard; Solodky, Sergei G. On the efficient discretization of integral equations of the third kind. J. Integral Equations Appl. 11 (1999), no. 4, 501–514.
Solodky, Sergei G. Complexity for some classes of well-posed problems. Proc. Estonian Acad. Sci. Phys. Math. 48 (1999), no. 2, 123–132.
Solodkiĭ, S. G. Optimization of projection methods for solving linear ill-posed problems. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 39 (1999), no. 2, 195--203; translation in Comput. Math. Math. Phys. 39 (1999), no. 2, 185–193
Solodky, S. G. A generalized projection scheme for solving ill-posed problems. J. Inverse Ill-Posed Probl. 7 (1999), no. 2, 185–200.
Solodkiĭ, S. G. A modification of a projection scheme for solving ill-posed problems. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 1998, no. 11, 83--90; translation in Russian Math. (Iz. VUZ) 42 (1998), no. 11, 79–86 (1999)
Solodkiĭ, S. G. On a discretization scheme for Fredholm equations of the first kind. (Russian) Differ. Uravn. 33 (1997), no. 11, 1547--1551, 1583; translation in Differential Equations 33 (1997), no. 11, 1551–1555 (1998)
Solodkiĭ, S. G. On an approach to the discretization of ill-posed problems. (Russian) Dokl. Akad. Nauk 356 (1997), no. 5, 608–611.
Solodkiĭ, S. G. An efficient approach to the M. M. Lavrentʹev discretization method. (Russian) Sibirsk. Mat. Zh. 38 (1997), no. 2, 396--404, iv; translation in Siberian Math. J. 38 (1997), no. 2, 342–349
Pereverzev, S. V.; Solodky, S. G. The minimal radius of Galerkin information for the Fredholm problem of the first kind. Special issue for the Foundations of Computational Mathematics Conference (Rio de Janeiro, 1997). J. Complexity 12 (1996), no. 4, 401–415.
Pereverzev, S. V.; Solodky, S. G. An efficient discretization for solving ill-posed problems. The mathematics of numerical analysis (Park City, UT, 1995), 643–649, Lectures in Appl. Math., 32, Amer. Math. Soc., Providence, RI, 1996.
Solodkiĭ, S. G. On the discretization of ill-posed problems. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 36 (1996), no. 8, 15--22; translation in Comput. Math. Math. Phys. 36 (1996), no. 8, 991–996 (1997)
Pereverzev, Sergei V.; Solodky, Sergei G. On optimization of direct methods of solving weakly singular integral equations. Festschrift for Joseph F. Traub, Part II. J. Complexity 9 (1993), no. 2, 313–325.
Perewersew, S. V.; Solodki, S. G. Optimierung direkter Verfahren für Gleichungen 2. Art mit Glättungsoperatoren. (German) [Optimization of direct methods for
equations of the second kind with smoothing operators] Math. Nachr. 153 (1991), 101–108.
Solodkiĭ, S. G. Optimization of adaptive direct methods for solving operator equations in a Hilbert space. (Russian) Ukrain. Mat. Zh. 42 (1990), no. 1, 95--102; translation in Ukrainian Math. J. 42 (1990), no. 1, 85–92
Pereverzev, Sergei V.; Solodky, Sergei G.; Volynets, Evgeny A. The balancing principle in solving semi-discrete inverse problems in Sobolev scales by Tikhonov method. Appl. Anal. 91 (2012), no. 3, 435–446.
Solodky, Sergei G.; Mosentsova, Ganna Unsaturable methods for solving severely ill-posed problems. Int. J. Comput. Sci. Math. 2 (2009), no. 3, 229–242.
Solodky, S. G.; Mosentsova, A. Morozov's discrepancy principle for the Tikhonov regularization of exponentially ill-posed problems. Comput. Methods Appl. Math. 8 (2008), no. 1, 86–98.
Solodky, S. G.; Lebedeva, E. V. On reduction of informational expenses in solving ill-posed problems with not exactly given input data. J. Inverse Ill-Posed Probl. 16 (2008), no. 2, 195–207
Lebedeva, E. V.; Solodkiĭ, S. G. On the approximation of finite-interval equations by piecewise-constant functions. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 48 (2008), no. 5, 731--745; translation in Comput. Math. Math. Phys. 48 (2008), no. 5, 693–706
Solodky, S. G.; Lebedeva, E. V. On reduction of informational expenses in solving ill-posed problems with not exactly given input data. J. Inverse Ill-Posed Probl. 16 (2008), no. 2, 195–207.
Solodkiĭ, S. G.; Lebedeva, E. V. On piecewise-constant discretization in the method of finite intervals. (Russian) Dokl. Akad. Nauk 416 (2007), no. 1, 36--39; translation in Dokl. Math. 76 (2007), no. 2, 786–789
Solodky, S. G.; Lebedeva, E. V. Error bounds of a fully discrete projection method for Symm's integral equation. Comput. Methods Appl. Math. 7 (2007), no. 3, 255–263.
Solodky, S. G. Economic discretization scheme for the nonstationary iterated Tikhonov method. J. Optim. Theory Appl. 132 (2007), no. 1, 21–39.
Solodky, Sergei G.; Lebedeva, Evgeniya V. Bounds of information expenses in constructing projection methods for solving ill-posed problems. Comput. Methods Appl. Math. 6 (2006), no. 1, 87–93.
Solodkiĭ, S. G. An algorithm for solving Fredholm equations with analytic coefficients. (Russian) Differ. Uravn. 41 (2005), no. 9, 1286--1290, 1296; translation in Differ. Equ. 41 (2005), no. 9, 1359–1363
Solodky, S. G. On a quasi-optimal regularized projection method for solving operator equations of the first kind. Inverse Problems 21 (2005), no. 4, 1473–1485.
Solodky, Sergei G. The optimal approximations for stationary iterated Tikhonov method. East J. Approx. 10 (2004), no. 1-2, 189–200.
Solodkiĭ, S. G. On a discretization scheme for the Landweber method. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 44 (2004), no. 3, 387--396; translation in Comput. Math. Math. Phys. 44 (2004), no. 3, 363–372
Solodkiĭ, S. G. Adaptive discretization of ill-posed problems. (Russian) Dokl. Akad. Nauk 382 (2002), no. 4, 460–462.
Solodky, S. G. The optimal approximations for solving linear ill-posed problems. J. Complexity 17 (2001), no. 1, 98–116.
Maaß, Peter; Pereverzev, Sergei V.; Ramlau, Ronny; Solodky, Sergei G. An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection. Numer. Math. 87 (2001), no. 3, 485–502.
Solodky, S. G. A generalized projection scheme for solving ill-posed problems. J. Inverse Ill-Posed Probl. 7 (1999), no. 2, 185–200.
Solodky, S. G. Complexity for some classes of equations of the second kind. Facta Univ. Ser. Math. Inform. No. 14 (1999), 159–169.
Pereverzev, Sergei V.; Schock, Eberhard; Solodky, Sergei G. On the efficient discretization of integral equations of the third kind. J. Integral Equations Appl. 11 (1999), no. 4, 501–514.
Solodky, Sergei G. Complexity for some classes of well-posed problems. Proc. Estonian Acad. Sci. Phys. Math. 48 (1999), no. 2, 123–132.
Solodkiĭ, S. G. Optimization of projection methods for solving linear ill-posed problems. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 39 (1999), no. 2, 195--203; translation in Comput. Math. Math. Phys. 39 (1999), no. 2, 185–193
Solodky, S. G. A generalized projection scheme for solving ill-posed problems. J. Inverse Ill-Posed Probl. 7 (1999), no. 2, 185–200.
Solodkiĭ, S. G. A modification of a projection scheme for solving ill-posed problems. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 1998, no. 11, 83--90; translation in Russian Math. (Iz. VUZ) 42 (1998), no. 11, 79–86 (1999)
Solodkiĭ, S. G. On a discretization scheme for Fredholm equations of the first kind. (Russian) Differ. Uravn. 33 (1997), no. 11, 1547--1551, 1583; translation in Differential Equations 33 (1997), no. 11, 1551–1555 (1998)
Solodkiĭ, S. G. On an approach to the discretization of ill-posed problems. (Russian) Dokl. Akad. Nauk 356 (1997), no. 5, 608–611.
Solodkiĭ, S. G. An efficient approach to the M. M. Lavrentʹev discretization method. (Russian) Sibirsk. Mat. Zh. 38 (1997), no. 2, 396--404, iv; translation in Siberian Math. J. 38 (1997), no. 2, 342–349
Pereverzev, S. V.; Solodky, S. G. The minimal radius of Galerkin information for the Fredholm problem of the first kind. Special issue for the Foundations of Computational Mathematics Conference (Rio de Janeiro, 1997). J. Complexity 12 (1996), no. 4, 401–415.
Pereverzev, S. V.; Solodky, S. G. An efficient discretization for solving ill-posed problems. The mathematics of numerical analysis (Park City, UT, 1995), 643–649, Lectures in Appl. Math., 32, Amer. Math. Soc., Providence, RI, 1996.
Solodkiĭ, S. G. On the discretization of ill-posed problems. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 36 (1996), no. 8, 15--22; translation in Comput. Math. Math. Phys. 36 (1996), no. 8, 991–996 (1997)
Pereverzev, Sergei V.; Solodky, Sergei G. On optimization of direct methods of solving weakly singular integral equations. Festschrift for Joseph F. Traub, Part II. J. Complexity 9 (1993), no. 2, 313–325.
Perewersew, S. V.; Solodki, S. G. Optimierung direkter Verfahren für Gleichungen 2. Art mit Glättungsoperatoren. (German) [Optimization of direct methods for
equations of the second kind with smoothing operators] Math. Nachr. 153 (1991), 101–108.
Solodkiĭ, S. G. Optimization of adaptive direct methods for solving operator equations in a Hilbert space. (Russian) Ukrain. Mat. Zh. 42 (1990), no. 1, 95--102; translation in Ukrainian Math. J. 42 (1990), no. 1, 85–92