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.
Subject:
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.
Biography
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.
M. Yu. Khristichenko, Yu. M. Nechepurenko, D. S. Grebennikov, G. A. Bocharov, “Numerical analysis of stationary solutions of systems with delayed argument in mathematical immunology”, CMFD, 68:4 (2022), 686–703
A. V. Boiko, K. V. Demyanko, S. V. Kirilovskiy, Yu. M. Nechepurenko, T. V. Poplavskaya, “Determination of threshold $N$-factors of the laminar-turbulent transition in a subsonic boundary layer on a prolate spheroid”, Prikl. Mekh. Tekh. Fiz., 62:6 (2021), 3–7; J. Appl. Mech. Tech. Phys., 62:6 (2021), 891–894
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.
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.
6.
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.
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.
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.
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; Comput. Math. Math. Phys., 58:5 (2018), 700–713
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
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.
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.
2015
14.
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.
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.
16.
Yu. M. Nechepurenko, “Hermitian Spectral Pseudoinversion and Its Applications”, Mat. Zametki, 96:1 (2014), 101–115; Math. Notes, 96:1 (2014), 110–121
17.
K. V. Demyanko, Yu. M. Nechepurenko, “Bi-Newton's method for computing spectral projectors”, Num. Meth. Prog., 15:1 (2014), 121–129
2010
18.
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; Comput. Math. Math. Phys., 50:11 (2010), 1914–1924
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; Comput. Math. Math. Phys., 50:6 (2010), 1055–1070
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; Comput. Math. Math. Phys., 48:5 (2008), 707–723
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; Comput. Math. Math. Phys., 46:7 (2006), 1155–1167
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; Math. Notes, 78:5 (2005), 669–676
2004
25.
Yu. M. Nechepurenko, M. Sadkane, “Convergence of the Newton–Kantorovich Method for Calculating Invariant Subspaces”, Mat. Zametki, 75:1 (2004), 109–114; Math. Notes, 75:1 (2004), 101–106
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; Comput. Math. Math. Phys., 44:5 (2004), 771–780
Yu. M. Nechepurenko, M. Sadkane, “The Newton–Kantorovich method for computing invariant subspaces”, Zh. Vychisl. Mat. Mat. Fiz., 43:11 (2003), 1627–1641; Comput. Math. Math. Phys., 43:11 (2003), 1564–1579
2002
28.
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; Math. Notes, 71:2 (2002), 211–216
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; Comput. Math. Math. Phys., 42:9 (2002), 1341–1345
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; Comput. Math. Math. Phys., 42:6 (2002), 739–746
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; Comput. Math. Math. Phys., 42:2 (2002), 125–134
S. K. Godunov, Yu. M. Nechepurenko, “On the annular separation of a matrix spectrum”, Zh. Vychisl. Mat. Mat. Fiz., 40:7 (2000), 980–985; Comput. Math. Math. Phys., 40:7 (2000), 939–944
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; Comput. Math. Math. Phys., 40:1 (2000), 32–39
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