The classical scalar Nevanlinna-Pick interpolation problem has a long and distinguished history, appearing in a variety of applications in mathematics and electrical engineering. There is a vast literature on this problem and on its various far reaching generalizations; for a quick historical survey see [1] and [38]. It is widely known that the now classical algorithm for solving this problem p...

We discuss the aysmptotics of the points that maximize the determinant of the interpolation matrix for interpolants of the form I1(x) = n ∑ i=1 aie αxti and I2(x) = n ∑

We will now dig deeper into the details of this matrix factorization, and discuss the two specific bilateral representations we use: the simplified bilateral grid, and the permutohedral lattice [1]. Filtering with both the permutohedral lattice and the simplified bilateral grid works by “splatting” a value at each pixel onto a small number of vertices, performing a separable blur in the space o...

The main topics of this technical report are quaternions, their mathematical properties, and how they can be used to rotate objects. We introduce quaternion mathematics and discuss why quaternions are a better choice for implementing rotation than the well-known matrix implementations. We then treat di erent methods for interpolation between series of rotations. During this treatment we give co...

In this paper, we consider a broad class of interpolation problems, for both scalarand vector-valued multivariate functions subject to linear side conditions, such as being divergence-free, where the data are generated via integration against compactly supported distributions. We show that, by using certain families of matrix-valued conditionally positive definite functions, such interpolation ...

B-splines provide an accurate and efficient method for interpolating regularly spaced data. In this paper, I study the applicability of B-spline interpolation in the context of the inverse interpolation method for regularizing irregular data. Numerical tests show that, in comparison with lower-order linear interpolation, B-splines lead to a faster iterative conversion in under-determined proble...