1,720,975 research outputs found
A Recursive algorithm by the moments method to evaluate a class of numerical integrals over an infinite interval
No full textA special recursive algorithm is built by a three-term recursive formula with coefficients evaluated by the moments method. A new functional c(·) is studied over any function space that contains the polynomial space and it is shown that such a functional is positive definite, enabling us to use the advantages of such a property on the zeros of orthogonal polynomials for such a functional. A comparison is presented of the numerical advantages of such a method with respect to the Laguerre polynomials
The modified bordering method to evaluate eigenvalues and eigenvectors of normal matrices.
No full textA bordering procedure is here proposed to evaluate the eigensystem of hermitian matrices, and more in general of normal matrices, when the spectral decomposition is known of then–1×n–1 principal minor. The procedure is also applicable to special real and nonsymmetric matrices here named quasi-symmetric. The computational cost to write the characteristic polynomial isO(n 2), using a new set of recursive formulas. A modified Brent algorithm is used to find the roots of the polynomial. The eigenvectors are evaluated in a direct way with a computational cost ofO(n 2) for each one. Some numerical considerations indicate where numerical difficulties may occur. Numerical results are given comparing this method with the Givens-Householder one
Polynomials arising in factoring generalized Vandermonde determinants III :computation of their roots
No full textReference Functional and Characteristic Space for Lagrange and Bernstein Operators
No full textThis paper deals with the description and the representation of polynomials defined, over n-simplices. The polynomials are computed by using two recurrent schemes, the Neville-Aitken one for the Lagrange interpolating operator and the De Casteljau one for the Bernstein-Bézier approximating operator. The concepts of reference functionals and characteristic spaces will be used and we shall prove the existence of a characteristic space for the reference functionals associated with these operators
Mathematical programming techniques to solve biharmonic problems by a recursive projection algorithm
Full text linkTo solve a classical ill-conditioned problem in the sense of Hadamard as the initial Cauchy problem for a
biharmonic operator after some a priori estimates, a posteriori estimates are evaluated using three different methods of
minimization such as: linear programming, least squares and a recursive projection algorithm for least squares.
Numerical comparisons will be made on these three methods
A package for representing C^1 interpolating surfaces: Application to the lagoon of Venice's bed
No full textThe paper deals with the description of a method and the accompanying software, the package LABSUP, for representing C 1 interpolating surfaces. The application to the lagoon of Venice's bed is also proposed. The surfaces are built over the Delaunay triangulation and the polynomial patches used for the representation can be chosen among the Q 18 element, the Clough-Tocher or the Powell–Sabin finite elements or simply using global Bézier methods. The first three patches require the knowledge of the gradients at the nodes, or at least a suitable estimation of them. Therefore, interesting in itself is the derivative estimation process based on the minimization of the energy functional associated with the interpolant. For the representation of the lagoon of Venice's bed we only used the reduced Clough-Tocher finite element, due to the high number of points involved for which one needs to compute the Delaunay triangulation, and simply the partial derivatives of first order. A brief description of the software modules together with some graphical results of parts of the lagoon of Venice's bed are also presented
Numerical Evaluation of Special Integrals with Application to Contact Problems
No full textIn this paper we give several recurrence formulas for moments related to different weight functions. These formulas are used to carry out numerical integration within a domain corresponding to the whole positive real axis. The method is characterized by the presence of an exponential function into the weight term. A recursive algorithm has been implemented to generate weights and nodes for any number of integration points. Benefits of the procedure are shown for particular cases with comparison of results obtained by other integration rules. An interesting application of the proposed method to the numerical treatment of contact problem is shown
A new recursive algorithm for a Gaussian quadrature formula via orthogonal polynomials
No full textWe are presenting here a class of integrals that has shown its importance in quantum mechanics. It's the class of integrals where may assume all possible positive real values and the function is known only approximatively in a tabular form. To evaluate such integrals we use a classical gaussian quadrature formula for which we develop nodes and weights through a new general recursive algorithm using a set of orthogonal polynomials. Such orthogonal polynomials are obtained through a numerical method using a three terms recurrence relation. The numerical results of the algorithm are presented and a special attention is given to obtain a good number of significant digits
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