linear algebra; numerical linear algebra; iterative methods for linear and non linear systems; eigenvalues, eigenvectors; mathematical programming; nonlinear programming mathematical programming.
Subject:
Conditions of numerical stability of the factorization method for solving linear systems were obtained. A generalized conjugate gradient method for solving linear and non linear systems was proposed and theoretically proved. The convergence some conjugate gradient method for extremal eigevalues of a matrix was investigated. Two-sided bound of minimal eigenvalue of positive-definite matrix in the presence of restrictions was obtained. The base point method for solving non linear programming problemes was propose.
Biography
Graduated from Saint-Petersburg state marine technical university in 1967. Department of applyed mathematics and mathematical modeling. Ph.D. thesis was defended in 1980. Dr.Sci. thesis was defended in 1998. A list of my works contains more than 50 titles.
Main publications:
Vychislitelnaya ustoichivost matrichnoi progonki // Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, t. 17, # 2, M., Nauka, 1977.
Issledovanie skhodimosti odnogo obobschennogo metoda sopryazhennykh gradientov dlya opredeleniya ekstremalnykh sobstvennykh znachenii. Chislennye metody i voprosy organizatsii vychislenii // Zapiski nauchnykh seminarov LOMI, t. 111, L., Nauka, 1981.
Opredelenie ekstremalnykh sobstvennykh znachenii minimizatsiei funktsionalov spetsialnogo vida // Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, # 2, M., Nauka, 1985.
Organizatsiya vychislenii pri reshenii zadach prakticheskoi optimizatsii. Chislennye metody i voprosy organizatsii vychislenii // Zapiski nauchnykh seminarov LOMI, t. 229, L., Nauka, 1995.
Dvustoronnyaya otsenka minimalnogo sobstvennogo znacheniya polozhitelno opredelennoi matritsy pri nalichii ogranichenii. Chislennye metody i voprosy organizatsii vychislenii: XIV // Zapiski nauchnykh seminarov POMI, t. 268, SPb., Nauka, 2000.
G. V. Savinov, “Two-sided bounds of the smallest eigenvalue of a positive-definite matrix in the presence of restrictions”, Zap. Nauchn. Sem. POMI, 268 (2000), 181–184; J. Math. Sci. (N. Y.), 114:6 (2003), 1857–1859
G. V. Savinov, “Organization of computations in solving practical optimization problems”, Zap. Nauchn. Sem. POMI, 229 (1995), 268–274; J. Math. Sci. (New York), 89:6 (1998), 1764–1767
1985
3.
G. V. Savinov, “Determination of extremal eigenvalues by minimization of functionals of a special type”, Zh. Vychisl. Mat. Mat. Fiz., 25:2 (1985), 292–295; U.S.S.R. Comput. Math. Math. Phys., 25:1 (1985), 190–192
G. V. Savinov, “Convergence of a generalized method of conjugate gradients for the determination of the extremal eigenvalues of a matrix”, Zap. Nauchn. Sem. LOMI, 111 (1981), 145–150; J. Soviet Math., 24:1 (1984), 95–98
1978
5.
G. V. Savinov, “Generalized method of conjugate gradients for the solution of linear systems”, Zap. Nauchn. Sem. LOMI, 80 (1978), 181–188; J. Soviet Math., 28:3 (1985), 397–402
G. V. Savinov, “Numerical stability of a block triangular decomposition for a class of linear systems”, Zh. Vychisl. Mat. Mat. Fiz., 18:6 (1978), 1589–1593; U.S.S.R. Comput. Math. Math. Phys., 18:6 (1978), 230–235
1977
7.
G. V. Savinov, “Conjugate gradient method for systems of nonlinear equations”, Zap. Nauchn. Sem. LOMI, 70 (1977), 178–183; J. Soviet Math., 23:1 (1983), 2012–2017
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