Shutyaev, Victor Petrovich

Statistics Math-Net.Ru
Total publications: 18
Scientific articles: 18
Presentations: 2

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Associate professor
Doctor of physico-mathematical sciences (1999)
Speciality: 01.01.07 (Computing mathematics)
Birth date: 07.04.1957
Keywords: adjoint equations; perturbation methods; iterative algorithms; sensitivity theory; optimal control; data assimilation.


A series of studies have been made on the development of methods for investigating and numerical solving the quasilinear data assimilation problems, based on the adjoint equation theory, optimal control methods, and perturbation algorithms. The data assimilation problems are formulated as optimal control problems for the models governed by quasilinear evolution equations with the aim to identify the initial data and/or the right-hand-side (source)functions of the original equations. The neccessary optimality condition reduces the problem under consideration to the optimality system involving the original evolution problem, the adjoint problem, and the optimality condition (the last means that the Gateaux derivative of the cost functional equals zero). For linearized problem, by eliminating the state and adjoint variables, the optimality system is reduced to the only equation for the unknown function to be identified (the control function). This control equation has the form Lu=F, where L is a linear operator (called the control operator), u is the sought-for function, and the right-hand side F is determined by the input data. The properties of the control operators were studied, which are often symmetric, non-negative and compact. Based on the properties of the control operators, the solvability of linear and nonlinear data assimilation problems in a specific functional spaces is proved. To study the solvability of nonlinear data assimilation problems the successive approximation method is used. Using the spectral properties of the control operators, various iterative algorithms for solving the data assimilation problems are formulated and justified with optimal choice of iteration parameters. The convergence rate estimates are derived. The main results of this series are published in the author's book "Control operators and iterative algorithms in variational data assimilation problems (Moscow: Nauka, 2001).


Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State University in 1979. Ph.D. thesis was defended in 1983. D.Sci. thesis was defended in 1999.

Member of GAMM (Gesellschaft fur Angewandte Mathematik und Mechanik).

Main publications:
  • Marchuk G. I., Agoshkov V. I., Shutyaev V. I. Adjoint Equations and Perturbation Algorithms in Nonlinear Problems. New York: CRC Press, 1996. 275 p. (izdano v Rossii: M.: Nauka, 1993).
  • Shutyaev V. P. Operatory upravleniya i iteratsionnye algoritmy v zadachakh variatsionnogo usvoeniya dannykh. M.: Nauka, 2001. 239 s.
  • Shutyaev V. P. Ob usvoenii dannykh v shkale gilbertovykh prostranstv dlya kvazilineinykh evolyutsionnykh zadach // Differentsialnye uravneniya, 1998, 34(3), 383–389.
  • Shutyaev V. P. Iteratsionnye metody vosstanovleniya nachalnykh dannykh v singulyarno vozmuschennykh evolyutsionnykh zadachakh // ZhVM i MF, 1997, 37(9), 1078–1086.
  • Shutyaev V. P. O svoistvakh operatora upravleniya v odnoi zadache ob usvoenii dannykh i algoritmakh ee resheniya // Matematicheskie zametki, 1995, 57(6), 941–944.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. V. P. Shutyaev, E. I. Parmuzin, “Sensitivity of functionals of the solution of a variational data assimilation problem with simultaneous reconstruction of heat fluxes and the initial state for the sea thermodynamics model”, Sib. Zh. Vychisl. Mat., 23:4 (2020),  457–470  mathnet
2. V. P. Shutyaev, E. I. Parmuzin, “Sensitivity of functionals to observation data in a variational assimilation problem for the sea thermodynamics model”, Sib. Zh. Vychisl. Mat., 22:2 (2019),  229–242  mathnet  elib; Num. Anal. Appl., 12:2 (2019), 191–201  isi  scopus
3. V. P. Shutyaev, E. I. Parmuzin, “Stability of the optimal solution to the problem of variational assimilation with error covariance matrices of observational data for the sea thermodynamics model”, Sib. Zh. Vychisl. Mat., 21:2 (2018),  225–242  mathnet  elib; Num. Anal. Appl., 11:2 (2018), 178–192  isi  elib  scopus
4. G. I. Marchuk, V. P. Shutyaev, “Adjoint equations and iterative algorithms in problems of variational data assimilation”, Trudy Inst. Mat. i Mekh. UrO RAN, 17:2 (2011),  136–150  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S138–S152  isi  scopus
5. V. I. Agoshkov, E. I. Parmuzin, V. P. Shutyaev, “Numerical algorithm for variational assimilation of sea surface temperature data”, Zh. Vychisl. Mat. Mat. Fiz., 48:8 (2008),  1371–1391  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 48:8 (2008), 1293–1312  isi  scopus
6. V. P. Shutyaev, “On the solvability of an initial-boundary value problem for a quasilinear heat equation”, Differ. Uravn., 35:6 (1999),  809–812  mathnet  mathscinet; Differ. Equ., 35:6 (1999), 811–814
7. I. Yu. Gejadze, V. P. Shutyaev, “An optimal control problem of initial data restoration”, Zh. Vychisl. Mat. Mat. Fiz., 39:9 (1999),  1479–1488  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 39:9 (1999), 1416–1425
8. V. P. Shutyaev, “On data assimilation in a scale of Hilbert spaces for quasilinear evolution problems”, Differ. Uravn., 34:3 (1998),  383–389  mathnet  mathscinet; Differ. Equ., 34:3 (1998), 382–388
9. I. Yu. Gejadze, V. P. Shutyaev, “Substantiation of the perturbation method for a quasilinear heat-conduction problem”, Zh. Vychisl. Mat. Mat. Fiz., 38:6 (1998),  948–955  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 38:6 (1998), 909–915
10. V. P. Shutyaev, “Iterative method for initial-data reconstruction in singularly perturbed evolutionary problems”, Zh. Vychisl. Mat. Mat. Fiz., 37:9 (1997),  1078–1086  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 37:9 (1997), 1042–1050
11. E. I. Parmuzin, V. P. Shutyaev, “Algorithms for solving a problem of data assimilation”, Zh. Vychisl. Mat. Mat. Fiz., 37:7 (1997),  816–827  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 37:7 (1997), 792–803
12. V. P. Shutyaev, “Some properties of a control operator in the problem of data assimilation, and algorithms for its solution”, Differ. Uravn., 31:12 (1995),  2063–2069  mathnet  mathscinet; Differ. Equ., 31:12 (1995), 2035–2041
13. V. P. Shutyaev, “The properties of control operators in one problem on data control and algorithms for its solution”, Mat. Zametki, 57:6 (1995),  941–944  mathnet  mathscinet  zmath; Math. Notes, 57:6 (1995), 668–671  isi
14. V. P. Shutyaev, “Perturbation algorithm for one slightly nonlinear first-order hyperbolic problem”, Zh. Vychisl. Mat. Mat. Fiz., 33:8 (1993),  1209–1217  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 33:8 (1993), 1067–1075  isi
15. V. P. Shutyaev, “Properties of a solution of a conjugate equation in a nonlinear hyperbolic problem”, Differ. Uravn., 28:4 (1992),  706–715  mathnet  mathscinet; Differ. Equ., 28:4 (1992), 577–585
16. V. P. Shutyaev, “Perturbation method for a weakly nonlinear hyperbolic first order problem”, Mat. Zametki, 50:5 (1991),  156–158  mathnet  mathscinet  zmath; Math. Notes, 50:5 (1991), 1207–1208  isi
17. V. P. Shutyaev, “Justification of perturbation algorithm in a nonlinear hyperbolic problem”, Mat. Zametki, 49:4 (1991),  155–156  mathnet  mathscinet  zmath; Math. Notes, 49:4 (1991), 439–440  isi
18. V. P. Shutyaev, “Computation of a functional in a certain nonlinear problem using the adjoint equation”, Zh. Vychisl. Mat. Mat. Fiz., 31:9 (1991),  1278–1288  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 31:9 (1991), 8–16  isi

Presentations in Math-Net.Ru
1. Sensitivity and error propagation in a variational framework
F.-X. Le Dimet, V. P. Shutyaev, T. H. Tran
Междкнародная конференция, посвященная 90-летию со дня рождения Г. И. Марчука "Современные проблемы вычислительной математики и математического моделирования"
June 9, 2015 11:00   
2. О работах Г. И. Марчука в области вычислительной математики и ее приложений
V. I. Agoshkov, V. B. Zalesnyi, V. P. Shutyaev
Междкнародная конференция, посвященная 90-летию со дня рождения Г. И. Марчука "Современные проблемы вычислительной математики и математического моделирования"
June 8, 2015 17:30   

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