Schaback, Robert

[["dc.bibliographiccitation.firstpage","614"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","SIAM Journal on Numerical Analysis"],["dc.bibliographiccitation.lastpage","633"],["dc.bibliographiccitation.volume","56"],["dc.contributor.author","Cheung, Ka Chun"],["dc.contributor.author","Ling, Leevan"],["dc.contributor.author","Schaback, Robert"],["dc.date.accessioned","2020-12-10T18:37:20Z"],["dc.date.available","2020-12-10T18:37:20Z"],["dc.date.issued","2018"],["dc.identifier.doi","10.1137/16M1072863"],["dc.identifier.eissn","1095-7170"],["dc.identifier.issn","0036-1429"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/76915"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.title","^2hBConvergence of Least-Squares Kernel Collocation Methods"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1623"],["dc.bibliographiccitation.issue","13"],["dc.bibliographiccitation.journal","International Journal for Numerical Methods in Engineering"],["dc.bibliographiccitation.lastpage","1639"],["dc.bibliographiccitation.volume","80"],["dc.contributor.author","Ling, Leevan"],["dc.contributor.author","Schaback, Robert"],["dc.date.accessioned","2018-11-07T11:21:01Z"],["dc.date.available","2018-11-07T11:21:01Z"],["dc.date.issued","2009"],["dc.description.abstract","Choosing data points is a common problem for researchers who employ various meshless methods for solving partial differential equations. On the one hand, high accuracy is always desired: oil the other, ill-conditioning problems of the resultant matrices, which may lead to unstable algorithms, prevent some researchers from using meshless methods. For example, the optimal placements of source points in the method of fundamental solutions or of the centers in the radial basis functions method are always unclear. Intuitively, Such optimal locations will depend on many factors: the partial differential equations, the domain, the trial basis used (i.e. the employed method itself), the computational precisions, some user-defined parameters, and so on. Such complexity makes the hope of having an optimal centers placement unpromising. In this paper, we provide a data-dependent algorithm that adaptively selects centers based on all the other variables. Copyright (C) 2009 John Wiley & Sons, Ltd."],["dc.identifier.doi","10.1002/nme.2674"],["dc.identifier.isi","000272938900001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/55680"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","John Wiley & Sons Ltd"],["dc.relation.issn","0029-5981"],["dc.title","An improved subspace selection algorithm for meshless collocation methods"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","339"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Advances in Computational Mathematics"],["dc.bibliographiccitation.lastpage","354"],["dc.bibliographiccitation.volume","30"],["dc.contributor.author","Lee, Cheng-Feng"],["dc.contributor.author","Ling, Leevan"],["dc.contributor.author","Schaback, Robert"],["dc.date.accessioned","2018-11-07T08:30:02Z"],["dc.date.available","2018-11-07T08:30:02Z"],["dc.date.issued","2009"],["dc.description.abstract","In this paper, we are interested in some convergent formulations for the unsymmetric collocation method or the so-called Kansa's method. We review some newly developed theories on solvability and convergence. The rates of convergence of these variations of Kansa's method are examined and verified in arbitrary-precision computations. Numerical examples confirm with the theories that the modified Kansa's method converges faster than the interpolant to the solution; that is, exponential convergence for the multiquadric and Gaussian radial basis functions (RBFs). Some numerical algorithms are proposed for efficiency and accuracy in practical applications of Kansa's method. In double-precision, even for very large RBF shape parameters, we show that the modified Kansa's method, through a subspace selection using a greedy algorithm, can produce acceptable approximate solutions. A benchmark algorithm is used to verify the optimality of the selection process."],["dc.identifier.doi","10.1007/s10444-008-9071-x"],["dc.identifier.isi","000264513100003"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/16799"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Springer"],["dc.relation.issn","1019-7168"],["dc.title","On convergent numerical algorithms for unsymmetric collocation"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1097"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","SIAM Journal on Numerical Analysis"],["dc.bibliographiccitation.lastpage","1115"],["dc.bibliographiccitation.volume","46"],["dc.contributor.author","Ling, Leevan"],["dc.contributor.author","Schaback, Robert"],["dc.date.accessioned","2018-11-07T11:20:46Z"],["dc.date.available","2018-11-07T11:20:46Z"],["dc.date.issued","2008"],["dc.description.abstract","In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of 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 meshless selection of test and trial spaces. The new method satisfies the assumptions of the background theory, and numerical experiments demonstrate its stability."],["dc.identifier.doi","10.1137/06067300X"],["dc.identifier.isi","000255500400001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/55617"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Siam Publications"],["dc.relation.issn","0036-1429"],["dc.title","Stable and convergent unsymmetric meshless collocation methods"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]