Analytical Approximation of the Blasius Similarity Solution with Rigorous Error Bounds

Lurupa - Rigorous Error Bounds in Linear Programming

Rigorous Error Bounds in Linear Programming Christian Keil Hamburg University of Te hnology, Institute for Reliable Computing .keil tu-harburg.de Abstra t. Linear Programming has numerous appli ations. Re ently it has been shown that many real world problems exhibit numeri al di ulties due to illonditioning. This paper des ribes Lurupa, a software pa kage for omputing rigorous bounds for the op...

Error Bounds for Approximation with Neural Networks

In this paper we prove convergence rates for the problem of approximating functions f by neural networks and similar constructions. We show that the rates are the better the smoother the activation functions are, provided that f satisses an integral representation. We give error bounds not only in Hilbert spaces but in general Sobolev spaces W m;r ((). Finally, we apply our results to a class o...

Rigorous Error Bounds for the Optimal Value in Semidefinite Programming

A wide variety of problems in global optimization, combinatorial optimization as well as systems and control theory can be solved by using linear and semidefinite programming. Sometimes, due to the use of floating point arithmetic in combination with ill-conditioning and degeneracy, erroneous results may be produced. The purpose of this article is to show how rigorous error bounds for the optim...

Error Bounds on the SCISSORS Approximation Method

The SCISSORS method for approximating chemical similarities has shown excellent empirical performance on a number of real-world chemical data sets but lacks theoretically proven bounds on its worst-case error performance. This paper first proves reductions showing SCISSORS to be equivalent to two previous kernel methods: kernel principal components analysis and the rank-k Nyström approximation ...

Rigorous error bounds for finite dimensional linear programming problems