We introduce a class of matrix-valued radial basis functions (RBFs) of compact support that can be customized, e.g. chosen to be divergence-free. We then derive and discuss error estimates for interpolants and derivatives based on these matrix-valued RBFs.
Radial basis functions (RBFs) have found important applications in areas such as signal processing, medical imaging, and neural networks since the early 1980's. Several applications require that certain physical properties are satisfied by the interpolant, for example being divergence free in case of incompressible data. In this paper we consider a class of… (More)
Approximation and interpolation employing radial basis functions has found important applications since the early 1980's in areas such as signal processing, medical imaging, as well as neural networks. Several applications demand that certain physical properties be fulfilled, such as a function being divergence free. No such class of radial basis functions… (More)
Recently a new class of customized radial basis functions (RBFs) was introduced. We revisit this class of RBFs and derive a density result guaranteeing that any sufficiently smooth divergence-free function can be approximated arbitrarily closely by a linear combination of members of this class. This result has potential applications to numerically solving… (More)
We present the combination of a sensor based on " Phase-Measuring Deflectometry " and a new numerical algorithm to obtain the shape of specular free-form surfaces. The sensor measures the local slope of the surface which then is used to reconstruct the object's shape. The sensor is calibrated and yields absolute slope data. We solved the inherent ambiguity… (More)
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