Control operators and iterative algorithms in problems of reconstructing source functions and initial data
Copyright policy )Control operators and iterative algorithms in problems of reconstructing source functions and initial data
Summary: We consider a data assimilation problem for linear and quasilinear evolution problems with the aim to reconstruct the right-hand side and initial data functions. We study the properties of a control operator in linear data assimilation problems and introduce fundamental control functions, which allow us to construct the solution of a linear optimal control problem in explicit form. Using the properties of the control operator, we prove solvability of linear and nonlinear problems in the scale of Hilbert spaces and for the case in which the original operator in an evolution problem may be nonsymmetric and time dependent. We consider the class of iterative algorithms, which are based on a simultaneous use of basic and adjoint equations, with the aim to solve the problems studied. Using the properties of control operators, we justify and optimize iterative processes, obtain estimates of the convergence rate.
Hilbert spaces, adjoint equations, Numerical optimization and variational techniques, convergence, inverse problems, iterative algorithms, eigenfunction expansion, linear data assimilation, Existence theories for optimal control problems involving partial differential equations, Numerical methods involving duality, Inverse problems in optimal control, linear optimal control, quasilinear evolution problems, Existence theories for problems in abstract spaces
Hilbert spaces, adjoint equations, Numerical optimization and variational techniques, convergence, inverse problems, iterative algorithms, eigenfunction expansion, linear data assimilation, Existence theories for optimal control problems involving partial differential equations, Numerical methods involving duality, Inverse problems in optimal control, linear optimal control, quasilinear evolution problems, Existence theories for problems in abstract spaces
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