MISFIT LANDFORMS IMPOSED BY ILL-CONDITIONED INVERSE PARAMETRIC PROBLEMS

Algebraic vs Analytic Design Limitations Imposed by Ill-Conditioned Plants

A long-standing conjecture has been that ill-conditioned multivariable plants pose inherent design di culty in achieving robust performance. The elusiveness of a proof of this conjecture has motivated study of an alternate design problem, involving only the nominal plant, in the hopes that an inherent di culty due to plant conditioning might emerge for this alternate problem. In this note we sh...

Ill-Posed and Linear Inverse Problems

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

Local Misfit Approximation in Memetic Solving of Ill-Posed Inverse Problems

Solving Inverse Problems by Decomposition, Classification and Simple Modeling: Extension to Ill-conditioned Cases

Inverse problems are found in many areas of science and engineering. It is usually difficult to approximate the inverse relationship due to the generally multi-valued and discontinuous nature. Several approaches to the solution of inverse problem have been proposed, but they are generally not applicable to situations and applications other than those they are developed for. In this thesis work,...

Error bounds for extremely ill-conditioned problems

We discuss methods to compute error bounds for extremely ill-conditioned problems. As a model problem we treat matrix inversion. We demonstrate that additive corrections to improve an approximate inverse are useful for ill-conditioned problems, but hardly usable for extremely ill-conditioned problems. Here multiplicative corrections can be used, including the possibility to compute guaranteed e...