1,721,105 research outputs found
Approximations on the Peano river network: Application of the Horton-Strahler hierarchy to the case of low connections
No full textA network analysis is used to investigate the low connections of natural river channels. At the basin scale, the river networks are analyzed according to the Horton-Strahler hierarchy. We propose a quantitative criterion for the average junction degree as a function of a fixed hierarchical order of the network and independent of the usual scaling laws. The numerical results of this analysis are compared with exact results of the Peano river network, showing differences of the order of 10-3. This aspect is especially relevant for the characterization of transport and diffusion processes at the basin scale. © 2009 The American Physical Society
A mixed interpolation-regression approximation operator on the triangle
Full text linkIn several applications, ranging from computational geometry and finite element analysis to computer graphics, there is a need to approximate functions defined on triangular domains rather than rectangular ones. For this purpose, frequently used interpolation methods include barycentric interpolation, piecewise linear interpolation, and polynomial interpolation. However, the use of polynomial interpolation methods may suffer from the Runge phenomenon, affecting the accuracy of the approximation in the presence of equidistributed data. In these situations, the constrained mock-Chebyshev least squares approximation on rectangular domains was shown to be a successful approximation tool. In this paper, we extend it to triangular domains, by using both Waldron and discrete Leja points. This paper is dedicated to Len Bos on the occasion of his retirement. Len, for us, is a master of mathematics and also a big friend. He introduced us to the fascinating world of "finding good interpolation no..
Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation
Full text linkExistence of sufficient conditions for unisolvence of Kansa unsymmetric collocation for PDEs is still an open problem. In this paper we make a first step in this direction, proving that unsymmetric collocation matrices with Thin-Plate Splines for the 2D Poisson equation are almost surely nonsingular, when the discretization points are chosen randomly on domains whose boundary has an analytic parametrization
The enriched multinode Shepard collocation method for solving elliptic problems with singularities
Full text linkIn this paper, the multinode Shepard method is adopted for the first time to numerically solve a differential problem with a discontinuity in the boundary. Starting from previous studies on elliptic boundary value problems, here the Shepard method is employed to catch the singularity on the boundary. Enrichments of the functional space spanned by the multinode cardinal Shepard basis functions are proposed to overcome the difficulties encountered. The Motz's problem is considered as numerical benchmark to assess the method. Numerical results are presented to show the effectiveness of the proposed approach
Activation of WNT and BMP signaling in adult human articular cartilage following mechanical injury
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An adaptive algorithm for determining the optimal degree of regression in constrained mock-Chebyshev least squares quadrature
Full text linkIn this paper we develop an adaptive algorithm for determining the optimal degree of regression in the constrained mock-Chebyshev least-squares interpolation of an analytic function to obtain quadrature formulas with high degree of exactness and accuracy from equispaced nodes. We numerically prove the effectiveness of the proposed algorithm by several examples
Numerical approximation of Fredholm integral equation by the constrained mock-Chebyshev least squares operator
Full text linkIn this paper, we propose two numerical approaches for approximating the solution of the following kind of integral equation f(y)−μ∫−11f(x)k(x,y)w(x)dx=g(y),y∈[−1,1],where f is the unknown solution, μ∈R∖{0}, k,g are given functions not necessarily known in the analytical form, and w is a Jacobi weight. The proposed projection methods are based on the constrained mock-Chebyshev least squares polynomials, and starting from data known at equally spaced points, provide a fine approximation of the solution. Such peculiarity can be helpful in all cases we deal with experimental data, typically measured at equispaced points. We prove the introduced methods are stable and convergent in some Sobolev subspace of C[−1,1]. Several numerical tests confirm the theoretical estimates and numerical effectiveness of the proposed method
Numerical differentiation on scattered data through multivariate polynomial interpolation
Full text linkWe discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor’s formula monomial basis. Error bounds for the approximation of partial derivatives of any order compatible with the function regularity are provided, as well as sensitivity estimates to functional perturbations, in terms of the inverse Vandermonde coefficients that are active in the differentiation process. Several numerical tests are presented showing the accuracy of the approximation
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