Optimal filtering for the backward heat equation
نویسنده
چکیده
For the backwards heat equation, stabilized by an a priori initial bound, an estimator is determined for intermediate values which is optimal with respect to the bound and the observation accuracy. It is shown how this may be implemented computationally with error estimates for the computed approximation which can be made arbitrarily close to the uncertainty level induced by the ill-posedness of the underlying problem. Thus, the feasibility of this for practical computation, inevitably severely limited by that inherent uncertainty, is as good as possible.
منابع مشابه
A regularization method for solving a nonlinear backward inverse heat conduction problem using discrete mollification method
The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...
متن کاملThree Dimensional Laminar Convection Flow of Radiating Gas over a Backward Facing Step in a Duct
In this study, three-dimensional simulations are presented for laminar forced convection flow of a radiating gas over a backward-facing step in rectangular duct. The fluid is treated as a gray, absorbing, emitting and scattering medium. The three-dimensional Cartesian coordinate system is used to solve the governing equations which are conservations of mass, momentum and energy. These equations...
متن کاملOptimal ltering for the backward heat equation 1
For the backwards heat equation, stabilized by an a priori initial bound, an estimator is determined for intermediate values which is optimal with respect to the bound and the observation accuracy. It is shown how this may be implemented computationally with error estimates for the computed approximation which can be made arbitrarily close to the uncertainty level induced by the ill-posedness o...
متن کاملSolving Differential Riccati Equations Using BDF Methods
This technical report describes three approaches for solving the Differential Riccati Equation (DRE), by means of the Backward Differentiation Formula (BDF) and resolution of the corresponding implicit equation, using Newton's method. These approaches are based on: GMRES method, resolution of Sylvester equation and fixed point method. The role and use of DRE is especially important in optimal c...
متن کاملMean-Variance Hedging and Forward-Backward Stochastic Differential Filtering Equations
and Applied Analysis 3 objective is min J v · ;x0 subject to v · ∈ Uad, x · ;v · satisfies 1.3 or 1.4 . PIMV The above problem formulates a mean-variance hedging problem with partial information. For simplicity, hereinafter we denote it by the notation “Problem PIMV ”, short for the “partial information mean-variance hedging problem”. In particular, if we let Ft Zt, 0 ≤ t ≤ T , then Problem PIM...
متن کامل