Inference from Inadequate and Inaccurate Data, II.
Having measured D numerical properties of a physical object E which requires many more than D parameters for its complete specification, an observer seeks to estimate P other numerical properties of E. A previous paper discussed how he can proceed when E is adequately described by one member m(E) of a Hilbert space [unk] of possible models of E and when all the observed and sought-for properties of E are Fréchet differentiable functionals on [unk]. The present paper describes a technique often available for reducing to this tractable case problems in which the functionals are discontinuous and are defined only on parts of [unk], and [unk] is an arbitrary real linear space. Applications include geophysical inverse problems and numerical differentiation, integration, interpolation, and extrapolation.
Backus
G
G
UNIVERSITY OF CALIFORNIA (LA JOLLA).