Optimal Filtering for the Backward Heat Equation

For the backward heat equation, stabilized by an a priori initial bound, an estimator is determined for intermediate values that 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 approximat...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1996-02, Vol.33 (1), p.162-170
Main Author: Seidman, Thomas I.
Format: Article
Language:English
Subjects:
A priori knowledge
Accuracy
Analytical estimating
Applied mathematics
Approximation
Calculus of variations and optimal control
Error rates
Estimate reliability
Estimates
Exact sciences and technology
Heat equation
Hilbert space
Ill posed problems
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Preliminary estimates
Sciences and techniques of general use
Semigroups
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Summary:For the backward heat equation, stabilized by an a priori initial bound, an estimator is determined for intermediate values that 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.
ISSN:0036-1429
1095-7170
DOI:10.1137/0733010