Multivariate piecewise linear interpolation of a random field Abstract We consider a multivariate piecewise linear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured by the integrated mean square error. Multivariate piecewise linear interpolator is defined by N field observations on a locations grid (or design). We investigate the class...

Efficient surface reconstruction and reverse engineering techniques are usually based on a polygonal mesh representation of the geometry: the resulting models emerge from piecewise linear interpolation of a set of sample points. The quality of the reconstruction not only depends on the number and density of the sample points but also on their alignment to sharp and rounded features of the origi...

In this paper, we show that the piecewise linear finite element solution uh and the linear interpolation uI have superclose gradient for tetrahedral meshes, where most elements are obtained by dividing approximate parallelepiped into six tetrahedra. We then analyze a post-processing gradient recovery scheme, showing that the global L2 projection of ∇uh is a superconvergent gradient approximatio...

In this paper, elasto-plastic analysis of an edge crack has been performed using element free Galerkin method. A model problem has been solved in plane stress condition under mode-I loading. A system of nonlinear equations has been obtained by using incremental theory of plasticity, and the equations are solved by assuming piecewise linear approximation. A code has been written in Matlab for el...

Using wetlands as sink of nutrients, phosphorus in particular, is becoming an increasingly attractive alternative to conventional wastewater treatment technology. In this paper, we brie y review the mechanism of phosphorus retention in wetlands, as well as previous modeling e orts. A Bayesian method is then proposed for estimating the long-term phosphorus accretion rate in wetlands through a pi...

We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional data. Except for a few special cases, this problem is hard to solve exactly, so we focus on heuristic methods that find locally optimal fits. The method we describe, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on d...

Classical Morse Theory [8] considers the topological changes of the level sets Mh = {x ∈ M | f(x) = h } of a smooth function f defined on a manifold M as the height h varies. At critical points, where the gradient of f vanishes, the topology changes. These changes can be classified locally, and they can be related to global topological properties of M . Between critical values, the level sets v...

This paper attempts to make an quantitative evaluation of available normalization techniques of matching scores in multimodal biometric systems. Two new normalization techniques Four Segments Piecewise Linear (FSPL) and Linear Tanh Linear (LTL) have been proposed in this paper. FSPL normalization techniques divides the region of genuine and impostor scores into four segments and maps each segme...

In this paper the problem of minimum cost communication network design is considered where the costs are piecewise linear concave. Several methods are compared: Simulated Annealing method, a heuristic based on the method proposed by Minoux, and a lagrangian method based on lower bounding procedure.