This is a short summary of recent mathematical results on error bounds and convergence of certain unsymmetric methods, including variations of Kansa’s collocation technique and Atluri’s MLPG method. The presentation is kept as simple as possible in order to address a larger community working on applications in Science and Engineering. Introduction and Summary The Meshless Local Petrov-Galerkin ...

In this paper we compare two recently proposed methods, FGMRES 5] and GMRESR 7], for the iterative solution of sparse linear systems with an unsymmetric nonsingular matrix. Both methods compute minimal residual approximations using preconditioners, which may be diierent from step to step. The insights resulting from this comparison lead to better variants of both methods.

In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. Kansa’s well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent m...

It takes two: A unique organocatalyzed cascade for the unsymmetric double arylation of α-nitrodiazoesters is described. This organocascade features the strategic use of carbene-activating anilines in conjunction with a urea catalyst, thus allowing for the synthesis of pharmaceutically attractive α-diarylesters through a transient NH insertion process.