Schaback, Robert

[["dc.bibliographiccitation.firstpage","77"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","CALCOLO"],["dc.bibliographiccitation.lastpage","87"],["dc.bibliographiccitation.volume","41"],["dc.contributor.author","Bozzini, M."],["dc.contributor.author","Lenarduzzi, L."],["dc.contributor.author","Rossini, M."],["dc.contributor.author","Schaback, Robert"],["dc.date.accessioned","2018-11-07T10:47:30Z"],["dc.date.available","2018-11-07T10:47:30Z"],["dc.date.issued","2004"],["dc.description.abstract","Under very mild additional assumptions, translates of conditionally positive definite radial basis functions allow unique interpolation to scattered multivariate data, because the interpolation matrices have a symmetric and positive definite dominant part. In many applications, the data density varies locally according to the signal behaviour, and then the translates should get different scalings that match the local data density. Furthermore, if there is a local anisotropy in the data, the radial basis functions should possibly be distorted into functions with ellipsoids as level sets. In such cases, the symmetry and the definiteness of the matrices are no longer guaranteed. However, this brief note is the first paper to provide sufficient conditions for the unique solvability of such interpolation processes. The basic technique is a simple matrix perturbation argument combined with the Ball-Narcowich-Ward stability results."],["dc.identifier.doi","10.1007/s10092-004-0085-6"],["dc.identifier.isi","000231278800002"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/47977"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Springer"],["dc.relation.issn","0008-0624"],["dc.title","Interpolation by basis functions of different scales and shapes"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","375"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Advances in Computational Mathematics"],["dc.bibliographiccitation.lastpage","387"],["dc.bibliographiccitation.volume","16"],["dc.contributor.author","Bozzini, M."],["dc.contributor.author","Lenarduzzi, L."],["dc.contributor.author","Schaback, Robert"],["dc.date.accessioned","2018-11-07T10:29:55Z"],["dc.date.available","2018-11-07T10:29:55Z"],["dc.date.issued","2002"],["dc.description.abstract","We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method."],["dc.identifier.doi","10.1023/A:1014584220418"],["dc.identifier.isi","000177900200005"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/43749"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Kluwer Academic Publ"],["dc.relation.issn","1019-7168"],["dc.title","Adaptive interpolation by scaled multiquadrics"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Numerical Algorithms"],["dc.bibliographiccitation.lastpage","16"],["dc.bibliographiccitation.volume","41"],["dc.contributor.author","Bozzini, M."],["dc.contributor.author","Lenarduzzi, L."],["dc.contributor.author","Schaback, Robert"],["dc.date.accessioned","2018-11-07T10:39:47Z"],["dc.date.available","2018-11-07T10:39:47Z"],["dc.date.issued","2006"],["dc.description.abstract","This paper applies difference operators to conditionally positive definite kernels in order to generate kernel B-splines that have fast decay towards infinity. Interpolation by these new kernels provides better condition of the linear system, while the kernel B-spline inherits the approximation orders from its native kernel. We proceed in two different ways: either the kernel B-spline is constructed adaptively on the data knot set X, or we use a fixed difference scheme and shift its associated kernel B-spline around. In the latter case, the kernel B-spline so obtained is strictly positive in general. Furthermore, special kernel B-splines obtained by hexagonal second finite differences of multiquadrics are studied in more detail. We give suggestions in order to get a consistent improvement of the condition of the interpolation matrix in applications."],["dc.identifier.doi","10.1007/s11075-005-9000-8"],["dc.identifier.isi","000234687500001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/46134"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Springer"],["dc.relation.issn","1017-1398"],["dc.title","Kernel B-splines and interpolation"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]