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Titlebook: Constructive Methods for the Practical Treatment of Integral Equations; Proceedings of the C G. Hämmerlin,K.-H. Hoffmann Conference proceed

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Optimal Discrepancy Principles for the Tikh0n0v Regularization of Integral Equations of the First Kon” of(1.1) Tx = y,i.e., the unique element that has minimal norm among all minimizers of the residual |Tx-y|. The best-approximate solution is actually given by T†y where T is the Moore-Penrose generalized inverse of T (see e.g. [15], [7]).
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On the Condition Number of Boundary Integral Equations in Acoustic Scattering using Combined Doubleme-harmonic acoustic scattering, can be resolved by seeking the solutions in the form of a combined double- and single-layer potential. We present an outline of an analysis of the appropriate choice of the coupling parameter in order to minimize the condition number of the integral equations.
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Solving Integral Equations on Surfaces in Space, operator is compact from C(S) into itself. We will consider a collocation method for numerically solving (1.1), with the approximating solution a function that is piecewise quadratic in a parameterization of the surface. The numerical method is of independent interest, but we have chosen the method
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