Rababah, Abedallah
July 2007
Computational Methods in Applied Mathematics;2007, Vol. 7 Issue 3, p221
Academic Journal
This paper presents methods to compute integrals of the Jacobi polynomials by the representation in terms of the Bernstein -- Bézier basis. We do this because the integration of the Bernstein -- Bézier form simply corresponds to applying the de Casteljau algorithm in an easy way. Formulas for the definite integral of the weighted Bernstein polynomials are also presented. Bases transformations are used. In this paper, the methods of integration enable us to gain from the properties of the Jacobi and Bernstein bases.


Related Articles

  • ON A CONVERGENT PROCESS OF BERNSTEIN. Szili, László; Vértesi, Péter // Publications de l'Institut Mathematique;2014, Vol. 96 Issue 110, p233 

    Bernstein in 1930 defined a convergent interpolation process based on the roots of the Chebyshev polynomials. We prove a similar statement for certain Jacobi roots.

  • An improved approximation scheme for the centrifugal term and the Hulthén potential. Ikhdair, S. M. // European Physical Journal A -- Hadrons & Nuclei;Mar2009, Vol. 39 Issue 3, p307 

    We present a new approximation scheme for the centrifugal term to solve the Schrödinger equation with the Hulthén potential for any arbitrary l -state by means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound-state energy eigenvalues and the normalized corresponding...

  • Numerical Integration over Spheres of Arbitrary Dimension. Brauchart, Johann S.; Hesse, Kerstin // Constructive Approximation;2007, Vol. 25 Issue 1, p41 

    In this paper we study the worst-case error (of numerical integration) on the unit sphere ${\Bbb S}^{d},\ d\geq 2,$ for all functions in the unit ball of the Sobolev space ${\Bbb H}^s({\Bbb S}^d),$ where $s>{d}/{2}.$ More precisely, we consider infinite sequences $(Q_{m(n)})_{n\in{\Bbb N}}$ of...

  • A stable algorithm for numerical inversion of system of generalized Abel integral equations. Dixit, Sandeep; Singh, Om Prakash // Journal of Advanced Research in Scientific Computing;2011, Vol. 3 Issue 4, p25 

    A direct method for stable inversion of system of generalized Abel integral equations is proposed using almost Bernstein operational matrix of integration.

  • An Adaptive Numerical Integration Algorithm with Automatic Result Verification for Definite Integrals. Storck, U. // Computing;2000, Vol. 65 Issue 3, p271 

    Presents a verified numerical integration algorithm with an adaptive strategy for smooth integrands. Verified representations of the remainder term; Distribution of the specified error bound onto the subintervals used in the algorithm; Numerical results.

  • RATIO OF PRICE TO EXPECTATION AT MAXIMAL INVESTMENT POINT. Yukio Hirashita // Far East Journal of Applied Mathematics;Sep2014, Vol. 88 Issue 3, p157 

    For a random payoff with positive expectation and negative infimum, a unique price exists at which the optimal proportion of investment reaches its maximum. For a random payoff with parallel translated value, the ratio of this price to its expectation tends to converge toward a value less than...

  • A TWO-STAGE ALGORITHM OF NUMERICAL EVALUATION OF INTEGRALS IN NUMBER-THEORETIC METHODS. Kai-tai Fang; Zu-kang Zheng // Journal of Computational Mathematics;May99, Vol. 17 Issue 3, p285 

    To improve the numerical evaluation of integrals in Number-Theoretic Methods, we give a two-stage algorithm. The main idea that we distribute the points according to the variations of the quadrature on the subdomains to reduce errors. The simulations results are also given.

  • Automatic numerical integration techniques for polyatomic molecules. Pérez-Jordá, José M.; Becke, Axel D.; San-Fabián, Emilio // Journal of Chemical Physics;5/1/1994, Vol. 100 Issue 9, p6520 

    We describe a new algorithm for the generation of 3D grids for the numerical evaluation of multicenter molecular integrals in density functional theory. First, we use the nuclear weight functions method of Becke [A. D. Becke, J. Chem. Phys. 88, 2547 (1988)] to decompose a multicenter integral...

  • Efficiency of different numerical methods for solving Redfield equations. Kondov, Ivan; Kleinekatho¨fer, Ulrich; Schreiber, Michael // Journal of Chemical Physics;1/22/2001, Vol. 114 Issue 4 

    The numerical efficiency of different schemes for solving the Liouville-von Neumann equation within multilevel Redfield theory has been studied. Among the tested algorithms are the well-known Runge-Kutta scheme in two different implementations as well as methods especially developed for time...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics