227 matrices based on cross-validation took roughly 12 min, with the main computational burden being the repeated evaluation and inversions of the 550 × 550 matrices G() and G(). Due to the increased computation time, finding the " optimal " and matrices in each step of the sequential algorithm appeared no longer practically feasible. When adding 450 additional function evaluations (based on th...

Stochastic methods of space-time interpolation and conditional simulation have been used in statistical downscaling approaches to increase the resolution of measured fields. One of the popular interpolation methods in geostatistics is kriging, also known as optimal interpolation in data assimilation. Kriging is a stochastic, linear interpolator which incorporates time/space variability by means...

An interpolation approach is pursued to solve a bilateral matrix polynomial equation frequently arising in control and signal processing. It results in eecient and numerically reliable resolution methods. Abstract New numerical procedures are proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal proces...

Interpolation or approximation of scattered data is very often task in engineering problems. The Radial Basis Functions (RBF) interpolation is convenient for scattered (un-ordered) data sets in k-dimensional space, in general. This approach is convenient especially for a higher dimension k > 2 as the conversion to an ordered data set, e.g. using tessellation, is computationally very expensive. ...

Radial Basis Functions (RBF) interpolation theory is briefly introduced at the “application level” including some basic principles and computational issues. The RBF interpolation is convenient for un-ordered data sets in n-dimensional space, in general. This approach is convenient especially for a higher dimension N 2 conversion to ordered data set, e.g. using tessellation, is computationally v...

Inpainting is a method for repairing damaged images or to remove unwanted parts of an image. While this process has been performed by professional artists in the past, today, the use of this technology is emerging in the medical area – especially in the medical imaging realm. In this study, the proposed inpainting method uses a radial basis function (RBF) interpolation technique. We first expla...

The consideration of elastic effects as well as nonlinear rigid body motions makes the description of mechanical systems by elastic multibody systems (EMBS) a powerful tool in the development process. Due to the fine spatial discretization of the elastic continuum, the reduction of the elastic degrees of freedom is necessary. This essential step to enable efficient EMBS simulations can be execu...

In [1] a balanced canonical form for continuoustime lossless systems was presented. This form has a tridiagonal dynamical matrix A and the useful property that the corresponding controllability matrix K is upper triangular. In [2], this structure is also derived from a LC ladder. In this paper, a connection is established between Ober’s canonical form and a Schur algorithm built from angular de...

When a mesh of simplicial elements (triangles or tetrahedra) is used to form a piecewise linear approximation of a function, the accuracy of the approximation depends on the sizes and shapes of the elements. In finite element methods, the conditioning of the stiffness matrices also depends on the sizes and shapes of the elements. This paper explains the mathematical connections between mesh geo...

We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpo...