Nechepurenko, Yuri Mihailovich

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Total publications: 36
Scientific articles: 35

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Senior Researcher
Doctor of physico-mathematical sciences (1997)
Speciality: 01.01.07 (Computing mathematics)
Birth date: 12.12.1959
E-mail: ,
Keywords: spectral analysis; integral performance creterions for dichotomy; separation of spectrum; spectral portraits; generalized Lyapunov equations; singular functions; transient regimes; reactivity; noncoservative systems; aeroelasticity problems; stability of hydrodynamic flows; modal analysis; measures of stability.


An interpolation approach to the construction of fast numerically stable algorithms was proposed for the matrix-vector multiplication. Analytical properties of singular functions of polynomial and analytical matrix pencils were been studied as well as the connection between the singular functions and spectral characteristics of the pencils. It was proposed the method of singular functions which reduces the eigenvalue problem for a matrix pencil to calculation of singular vectors corresponding to the smallest singular values of the pencil at fixed values of the parameter. It was proposed a new technology of numerical spectral analysis which is based on the Schur decomposition and required for a detailed spectral analysis of the ODE's system $du/dt=Au$ asymptotically $1/n$ arithmetic operations of the traditional technology, where $n$ means the order of the matrix $A$. New norm bounds for the matrix exponential and the Green matrix that significantly more precise than the known ones were obtained. A number of papers (in collaboration with S. K. Godunov) were concerned with methods based on the integral performance criterions for dichotomy. Particularly, a new approach to proofs of the existence of low-dimensional main parts was proposed for finite-dimensional analoges of the operators whose inverses exist and are finite-order operators according to Keldish's difinition. This approach is significantly simpler than traditional one (based on entire function theory) and makes possible to obtain more precise estimates of the resolvent norm. Based on the integral performance criterions for dichitomy new covergence rate estimates were obtained for a Newton method for computing invariant subspaces of finite-dimentional analoges of a partial differential operator. These estimates allow to connect the rate of convergence with properties of the initial operator which are usually studied in the theory of differential operators.


Graduated from Faculty of Physics and Energetics Problems of Moscow Institute of Physics and Technology (MIPT) in 1982. Ph. D. thesis was defended in 1986. D. Sci. thesis was defended in 1996. Lecturer at MIPT, lectures on "Spectral analysis of nonstationary systems". A list of my works contains more than 50 titles.

Main publications:
  • Nechepurenko Yu. M. On the singular-function approach to eigenproblems // Russian J. Numer. Anal. Math. Modelling, 1998, 13(3), 219–233.
  • Nechepurenko Yu. M. New spectral analysis technology based on the Schur decomposition // Russian J. Numer. Anal. Math. Modelling, 1999, 14(3), 265–274.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. G. V. Zasko, A. V. Glazunov, E. V. Mortikov, Yu. M. Nechepurenko, “Large-scale structures in stratified turbulent Couette flow and optimal disturbances”, Keldysh Institute preprints, 2019, 063, 31 pp.  mathnet  elib
2. E. V. Sklyarova, Yu. M. Nechepurenko, G. A. Bocharov, “Numerical steady state analysis of the Marchuk–Petrov model of antiviral immune response”, Keldysh Institute preprints, 2019, 031, 26 pp.  mathnet  elib
3. Yu. M. Nechepurenko, M. Yu. Khristichenko, D. S. Grebennikov, G. A. Bocharov, “Bistability analysis of virus infection models with delayed arguments”, Keldysh Institute preprints, 2019, 017, 26 pp.  mathnet  elib
4. Yu. M. Nechepurenko, M. Yu. Khristichenko, “Вычисление оптимальных возмущений для систем с запаздыванием”, Zh. Vychisl. Mat. Mat. Fiz., 59:5 (2019),  775–791  mathnet  elib
5. A. V. Boiko, K. V. Demyanko, Yu. M. Nechepurenko, “Asymptotic boundary conditions for the analysis of hydrodynamic stability of flows in regions with open boundaries”, Keldysh Institute preprints, 2018, 129, 27 pp.  mathnet  elib
6. Yu. M. Nechepurenko, M. Yu. Khristichenko, “Development and analysis of algorithms for computing optimal disturbances for delay systems”, Keldysh Institute preprints, 2018, 120, 26 pp.  mathnet  elib
7. A. V. Boiko, K. V. Demyanko, Yu. M. Nechepurenko, “Numerical analysis of spatial hydrodynamic stability of shear flows in ducts of constant cross section”, Zh. Vychisl. Mat. Mat. Fiz., 58:5 (2018),  726–740  mathnet  elib; Comput. Math. Math. Phys., 58:5 (2018), 700–713  isi  scopus
8. G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko, D. S. Grebennikov, “Optimal perturbations of systems with delayed argument for control of dynamics of infectious diseases based on multicomponent actions”, CMFD, 63:3 (2017),  392–417  mathnet
9. G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko, D. S. Grebennikov, “Control of models of virus infections with delayed variables, based on optimal disturbances”, Keldysh Institute preprints, 2017, 052, 28 pp.  mathnet
10. A. V. Boiko, K. V. Demyanko, D. A. Kuzmin, O. Mierka, Yu. M. Nechepurenko, L. P. Rivkind, “Numerical modeling of generation and propagation of Görtler vortices”, Keldysh Institute preprints, 2016, 048, 37 pp.  mathnet
11. A. V. Boiko, K. V. Demyanko, Yu. M. Nechepurenko, “On computing the location of laminar-turbulent transition in compressible boundary layers”, Keldysh Institute preprints, 2015, 081, 21 pp.  mathnet
12. A. V. Boiko, N. V. Klyushnev, Yu. M. Nechepurenko, “On stability of Poiseuille flow in a channel with surface ribbing”, Keldysh Institute preprints, 2014, 089, 20 pp.  mathnet
13. Yu. M. Nechepurenko, “Hermitian Spectral Pseudoinversion and Its Applications”, Mat. Zametki, 96:1 (2014),  101–115  mathnet  mathscinet  zmath  elib; Math. Notes, 96:1 (2014), 110–121  isi  scopus
14. K. V. Demyanko, Yu. M. Nechepurenko, “Bi-Newton's method for computing spectral projectors”, Num. Meth. Prog., 15:1 (2014),  121–129  mathnet
15. A. V. Boiko, Yu. M. Nechepurenko, M. Sadkane, “Fast computation of optimal disturbances for duct flows with a given accuracy”, Zh. Vychisl. Mat. Mat. Fiz., 50:11 (2010),  2017–2027  mathnet; Comput. Math. Math. Phys., 50:11 (2010), 1914–1924  scopus
16. A. V. Boĭko, Yu. M. Nechepurenko, “A technique for the numerical analysis of the riblet effect on the temporal stability of plane flows”, Zh. Vychisl. Mat. Mat. Fiz., 50:6 (2010),  1109–1125  mathnet  mathscinet; Comput. Math. Math. Phys., 50:6 (2010), 1055–1070  isi  scopus
17. Yu. M. Nechepurenko, G. V. Ovchinnikov, “Upper bounds for the solution norms of the Hermitian ODAE systems”, Ufimsk. Mat. Zh., 1:4 (2009),  125–132  mathnet  zmath
18. A. V. Boiko, Yu. M. Nechepurenko, “Numerical spectral analysis of temporal stability of laminar duct flows with constant cross sections”, Zh. Vychisl. Mat. Mat. Fiz., 48:10 (2008),  1731–1747  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 48:10 (2008), 1699–1714  isi  scopus
19. I. A. Karasëva, Yu. M. Nechepurenko, A. S. Potyagalova, “Spectral reduction for control systems modeling passive integrated circuits”, Zh. Vychisl. Mat. Mat. Fiz., 48:5 (2008),  746–762  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 48:5 (2008), 707–723  isi  scopus
20. R. S. Martynov, Yu. M. Nechepurenko, “Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system”, Zh. Vychisl. Mat. Mat. Fiz., 46:7 (2006),  1219–1231  mathnet  mathscinet; Comput. Math. Math. Phys., 46:7 (2006), 1155–1167  scopus
21. Yu. M. Nechepurenko, “Integral Criteria for the Quality of the Dichotomy of a Matrix Spectrum by a Closed Contour”, Mat. Zametki, 78:5 (2005),  718–726  mathnet  mathscinet  zmath  elib; Math. Notes, 78:5 (2005), 669–676  isi  scopus
22. Yu. M. Nechepurenko, M. Sadkane, “Convergence of the Newton–Kantorovich Method for Calculating Invariant Subspaces”, Mat. Zametki, 75:1 (2004),  109–114  mathnet  mathscinet  zmath; Math. Notes, 75:1 (2004), 101–106  isi
23. R. S. Martynov, Yu. M. Nechepurenko, “Finding a response matrix for a discrete linear dynamic stochastic system”, Zh. Vychisl. Mat. Mat. Fiz., 44:5 (2004),  817–826  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 44:5 (2004), 771–780
24. Yu. M. Nechepurenko, M. Sadkane, “The Newton–Kantorovich method for computing invariant subspaces”, Zh. Vychisl. Mat. Mat. Fiz., 43:11 (2003),  1627–1641  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 43:11 (2003), 1564–1579
25. Yu. M. Nechepurenko, “Estimates for the Norm of Green's Matrix Based on the Integral Performance Criterion for Dichotomy and Hausdorff Set Bounds”, Mat. Zametki, 71:2 (2002),  232–238  mathnet  mathscinet  zmath; Math. Notes, 71:2 (2002), 211–216  isi  scopus
26. Yu. M. Nechepurenko, L. K. Shishkov, “Determination of a reactivity based on the inverse point kinetics equation”, Zh. Vychisl. Mat. Mat. Fiz., 42:9 (2002),  1394–1398  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 42:9 (2002), 1341–1345
27. S. K. Godunov, Yu. M. Nechepurenko, “Bounds for the convergence rate of Newton's method for calculating invariant subspaces”, Zh. Vychisl. Mat. Mat. Fiz., 42:6 (2002),  771–779  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 42:6 (2002), 739–746
28. Yu. M. Nechepurenko, “Bounds for the matrix exponential based on the Lyapunov equation and limits of the Hausdorff set”, Zh. Vychisl. Mat. Mat. Fiz., 42:2 (2002),  131–141  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 42:2 (2002), 125–134
29. S. K. Godunov, Yu. M. Nechepurenko, “On the annular separation of a matrix spectrum”, Zh. Vychisl. Mat. Mat. Fiz., 40:7 (2000),  980–985  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 40:7 (2000), 939–944
30. S. K. Godunov, Yu. M. Nechepurenko, “Bounds for the principal and stiff components based on the integral performance criterion for dichotomy”, Zh. Vychisl. Mat. Mat. Fiz., 40:1 (2000),  35–42  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 40:1 (2000), 32–39
31. Yu. M. Nechepurenko, “An implicit exhaustion method for partial generalized eigenvalue problems”, Zh. Vychisl. Mat. Mat. Fiz., 35:7 (1995),  1022–1033  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 35:7 (1995), 815–823  isi
32. Yu. M. Nechepurenko, “The singular-function method for computing the eigenvalues of polynomial matrices”, Zh. Vychisl. Mat. Mat. Fiz., 35:5 (1995),  646–660  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 35:5 (1995), 507–517  isi
33. Yu. M. Nechepurenko, “A polynomially stable fast parallel algorithm for tridiagonal systems”, Zh. Vychisl. Mat. Mat. Fiz., 26:7 (1986),  963–969  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 26:4 (1986), 1–5
34. Yu. M. Nechepurenko, “Numerical stability of the marching method”, Zh. Vychisl. Mat. Mat. Fiz., 25:1 (1985),  3–11  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 25:1 (1985), 1–7
35. Yu. M. Nechepurenko, “A factorization of elements of an inverse matrix”, Zh. Vychisl. Mat. Mat. Fiz., 24:4 (1984),  601–605  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 24:2 (1984), 172–175

36. Yu. M. Nechepurenko, “Letter to the Editor”, Mat. Zametki, 72:2 (2002),  320  mathnet  mathscinet; Math. Notes, 72:2 (2002), 291  isi  scopus

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