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By Pierluigi Crescenzi, Viggo Kann.

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Applies if one starts with A similar argument d—=■ w being of one sign and moreorless ax constant, and then chooses a corresponding W satisfying the boundary condition (11). The example shows that some form of stabilization should be introduced into the evaluation of Tn. This point will be pursued elsewhere (Hoffmann and Anderssen (1987)). The Inverse Problem of Aquifer Transmissivity Identification 27 The advantages of the methodology (ii) are: (a) the flexibility in the choice of W allows one to test the hypothesis that T ~ const.

O m are a basis for the null space of Jm in Ψ™, namely, the polynomials of in W™. Suppose it is desired to allow g εΗ to have degree less than m, and Hl=N(Jm)1 a jump in the first derivative at x*. Then we let p = l and x¥l(x) = \x -x*\. Then, if feW% withm>2andg = / +ΘΨ 1? 3t ax dx = 2Θ. More generally, to include a jump in the fcth derivative, we can let the M^'s be of the form ΨΛ = — , for k

Nashed characterization aspects of the notions of regularizers introduced. , what corresponds to a "regularizing parameter" and its choice in the present setting) will be addressed in another paper. 2. ON THE ROLE OF OUTER INVERSES IN "SOLVABILITY" AND "REGULAJRIZATION" OF ILL-POSED PROBLEMS In this section we illustrate the role and properties of outer inverses for approximate solutions of ill-posed problems in standard and familiar settings. 1. Regularizers Are Never Inner Inverses Inner inverses are connected with solvability of the equation Af = g.

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A Compendium of NP Optimization Problems by Pierluigi Crescenzi, Viggo Kann.

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