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Optimal estimation of linear operators from inaccurate data: A second look

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Abstract

This paper intends to re-examine some results and proofs given in a previous publication on optimal estimation under uncertainty. In a rather general setting we showed that regularization of an element of a linear space relative to a quadratic criterion and inaccurate linear observations is an optimal method for recovering a linear operator of that element. For this to be the case, the regularization parameter must be chosen with care.

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  1. IBM Research Division, T.J. Watson Research Center, 10598, Yorktown Heights, NY, USA

    Charles A. Micchelli

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  1. Charles A. Micchelli
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Micchelli, C.A. Optimal estimation of linear operators from inaccurate data: A second look. Numer Algor 5, 375–390 (1993). https://doi.org/10.1007/BF02109419

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