Electronic Resource
Springer
Journal of optimization theory and applications
32 (1980), S. 521-536
ISSN:
1573-2878
Keywords:
Optimal filters
;
variational problems
;
renewal equations
;
existence and uniqueness
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A class of filter problems in which the autocorrelation function of the noise is assumed to be expressible as a convolution is related to a variational problem. The variational problem involves the minimization of the square of theL 1[0, ∞] norm of a function y plus the square of theL 2[0, ∞] norm of a functionG. The functions y andG are related by a renewal equation. The problems formulated here include as special cases previous problems solved by the authors and their students. In the present paper, the existence and uniqueness of the solution of the variational problems are established.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934038
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