Parallel Computing Developed an algorithm for orthogonal reduction of dense matrices to bidiagonal form on computers with distributed memory architectures. Created the code intended for bidiagonalization of square complex matrix. Worked on PSPARSLIB: a library of FORTRAN subroutines for solving large sparse linear systems in parallel in collaboration with Dr. Yousef Saad (http://www.cs.umn.edu/Research/arpa/p_sparslib/psp-abs.html). Krylov methods Proposed jointly with S. K. Godunov and J.-F. Carpraux the definition of condition numbers for the Krylov bases and subspaces. Obtained perturbation bounds of the orthogonal basis of the Krylov subspace as well as perturbation bounds of Hessenberg form of a matrix with respect to arbitrary perturbations in the matrix and in the initial vector. QR method Investigated the problem of convergence of the orthogonal power and QR algorithm (with prof. Godunov S. K.). The investigation is devoted to effect of round off errors on convergence of the orthogonal power method. Numerical methods for ordinary differential equations Developed the method of estimating the state of a process from measurements. The process is described by a system of ordinary differential equations with a vector stochastic process in the right-hand side. Suggested a new stable algorithm for finding efficient and some other estimates. Developed a new version of the orthogonal factorization method and proved its stability, which has been first proposed by S. K. Godunov Proposed the algorithm for calculating integral curves connecting a given two stationary points of a system of differential equations and its associated parameter values based on the new version of the orthogonal factorization method.

August 1997 — present, Senior researcher, Institute of Mathematics, Novosibirsk, Russia. Conducting research on parallel and distributed computing and numerical analysis. 1996 – August 97 University of Minnesota, Research Associate, Department of Computer Science and Minesota Supercomputer Center, Minneapolis, MN. Conducted research on parallel and distributed computing. 1995–1996 Participant of the Boeing Company project, Keldysh Institute of Applied Mathematics and the Boeing Company, Moscow, Russia Applied linear algebra to the problem of construction of block-structured quadrangular grids on plane and surface. April 1995 – July 1995, March 1996 – May 1996 Visiting scientist, IRISA/INRIA, Rennes, France As a member of COPERNICUS project, conducted research on parallel and distributed computing. 1986–1992 Researcher, 1992–1996 Senior researcher, Institute of Mathematics, Novosibirsk, Russia. 1982–1984 Graduate Program, 1984–1986 Probationer-researcher, Institute of Mathematics, Novosibirsk, Russia (advisor Prof. S. K. Godunov). Conducted research on numerical linear algebra and numerical methods for differential equations.

Other activities Associate Editor for journal "Parallel Computing", Elsevier Science. Referee of journals: "Parallel computing", "Linear Algebra and Applications", "Siberian Mathematical Journal", "Numerical Methods and Its Applications" and etc. Member of Council on High Performance Computing in Siberian Branch of Russian Academy of Science.

• J. F. Carpraux, S. Godunov, S. Kuznetsov. Condition number of the Krylov bases and subspaces // Linear Algebra and its Applications, Elsevier Science, v. 248, p. 137–161, 1996.
• S. Kuznetsov. Perturbation Bounds of The Krylov Bases and Associated Hessenberg Forms // Linear Algebra and its Applications, Elsevier Science, v. 265, p. 1–28, 1997.
• S. Kuznetsov. Orthogonal reduction of dense matrices to bidiagonal form on computers with distributed memory architectures // Parallel Computing, Elsevier Science, v. 24/2, p. 305–313, 1998.
• S. Kuznetsov, G. C. Lo, and Y. Saad. Parallel solution of general sparse linear systems // Domain Decomposition XI, editors: Choi-Hong Lai, Petter Bjorstad, Mark Cross, and Olof B. Widlund. Domain Decomposition Press, Bergen, Norway, p. 455–465, 1999.
• Godunov S. K., Kuznetsov S. Estimates for the convergence of the orthogonal power method // Siberian Advances in Mathematics, v. 5, no. 1, p. 16–42, Alerton Press, New-York, 1995.

• Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk