Solving the so-called geodesic endpoint problem, i.e., finding a that connects two given points on manifold, is at basis of virtually all data processing operations, including averaging, clustering, interpolation and optimization. On Stiefel manifold orthonormal frames, this problem computationally involved. A remedy to use quasi-geodesics as replacement for Riemannian geodesics. Quasi-geodesic...

The first soft-decision decoding algorithm for algebraic–geometric codes is presented. This algorithm is developed based on the Koetter-Vardy algorithm, which was proposed for the decoding of Reed-Solomon codes. The interpolation process is modified by redefining the zero condition of a trivariate polynomial and introducing complexity reducing methods. Simulation results show that 0.7 and 1.7 d...

In this paper, several modiications of the quasi-interpolation operator of Scott and Zhang (Math. Comp. 54(1990)190, 483{493) are discussed. The modiied operators are deened for non-smooth functions and are suited for the application on anisotropic meshes. The anisotropy of the elements is reeected in the local stability and approximation error estimates. As an application, an example is consid...

Inspired by the notion of biconic semi-copulas, we introduce biconic semi-copulas with a given section. Such semi-copulas are constructed by linear interpolation on segments connecting the graph of a continuous and decreasing function to the points (0, 0) and (1, 1). Special classes of biconic semi-copulas with a given section such as biconic (quasi-)copulas with a given section are considered....

We propose a new quadrature rule for Cauchy principal value integrals based on quadratic spline quasi-interpolants which have an optimal approximation order and satisfy boundary interpolation conditions. In virtue of these spline properties, we can prove uniform convergence for sequences of such quadratures and provide uniform error bounds. A computational scheme for the quadrature weights is g...

In this paper we generalize several results on uniform approximation orders with radial basis functions in (Buhmann, Dyn and Levin, 1993) and (Dyn and Ron, 1993) to L-approximation orders. These results apply, in particular, to approximants from spaces spanned by translates of radial basis functions by scattered centres. Examples to which our results apply include quasi-interpolation and least-...

In this paper, we are interested in deriving a non-intrusive numerical approach to construct nonlinear and linear parameter varying reduced order models from data. More specifically, based on data collected stable non-linear time-domain simulator or experimental bench, show how can infer either (quasi) dependent model. The proposed is very recent procedure called MII for Mixed Interpolation Inf...

On a Bakhvalov-type mesh widely used for boundary layers, we consider the finite element method singularly perturbed elliptic problems with two parameters on unit square. It is very challenging task to analyze uniform convergence of this in 2D. The existing analysis tool, quasi-interpolation, only applicable one-dimensional case because complexity In paper, powerful Lagrange-type interpolation,...