177 research outputs found

    On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations

    Get PDF
    It is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled nodes. The chord method is an interpolatory method, with two distinct nodes. Using this remark, the Steffensen and Aitken-Steffensen methods have been generalized using interpolatory methods obtained from the inverse interpolation polynomial of Lagrange or Hermite type. In this paper we study the convergence and efficiency of some Steffensen type methods which are obtained from the inverse interpolatory polynomial of Hermite type with two controlled nodes

    Series Prediction based on Algebraic Approximants

    Get PDF
    It is described how the Hermite-Pad\'e polynomials corresponding to an algebraic approximant for a power series may be used to predict coefficients of the power series that have not been used to compute the Hermite-Pad\'e polynomials. A recursive algorithm is derived and some numerical examples are given.Comment: 9 pages, ISRN Applied Mathematics, in pres

    Subresultants in Multiple Roots

    Get PDF
    We extend our previous work on Poisson-like formulas for subresultants in roots to the case of polynomials with multiple roots in both the univariate and multivariate case, and also explore some closed formulas in roots for univariate polynomials in this multiple roots setting.Comment: 21 pages, latex file. Revised version accepted for publication in Linear Algebra and its Application

    An algorithm for the quadratic approximation

    Get PDF
    The quadratic approximation is a three dimensional analogue of the two dimensional Pade approximation. A determinantal expression for the polynomial coefficients of the quadratic approximation is given. A recursive algorithm for the construction of these coefficients is derived. The algorithm constructs a table of quadratic approximations analogous to the Pade table of rational approximations

    An algorithm for the quadratic approximation

    Get PDF
    The quadratic approximation is a three dimensional analogue of the two dimensional Pade approximation. A determinantal expression for the polynomial coefficients of the quadratic approximation is given. A recursive algorithm for the construction of these coefficients is derived. The algorithm constructs a table of quadratic approximations analogous to the Pade table of rational approximations

    Abstracts of CSc. theses in mathematics

    Get PDF
    summary:Pham, Huu Uyen: Semilinear structure of a-languages. Havlas, Josef: N-ary semiheaps. Charamza, Pavel: Isotonic regression and stochastic approximation. Koukal, Stanislav: Piecewise rational interpolations in the use for solving elliptic boundary value problems. Dontová, Eva: Reflexion function and the Dirichlet and Neumann problems. Kopincová, Edita: Methods of geometrical modelling with the reference to the ruled surfaces of revolution. Slovák, Jan: Natural bundles and operators on some categories. Matouček, Jiří: Lipschitz distances of metric spaces. Loebl, Martin: Rapidly growing functions. Ambrož, Luděk: Quasiconvex and pseudoconvex functions in mathematical programming. Fiala, Jiří: Hermite-Birkhoff interpolation. Pokorná, Olga: Spinor fields on Riemannian manifolds. Budínský, Petr: Interpolation in multidimensional random sequences. Hanousek, Jan: Robust Bayesian type estimators. Peregrin, Jaroslav: A general theory of semantics of languages of formal logic. Drózd, Januš: A new method of parsing by recursive descent for LR(k)LR(k) grammars. Polák, Jaroslav: Aggregation and disaggregation in Markov chains. Hála, Martin: Random eigenvalue problems for ordinary equations with random coefficients Savický, Petr: Random Boolean formulas. Klouček, Petr: Time stabilization of the artificial compressibility method for the solution of the transonic flow problem

    Polynome, Interpolation, Splines und Differentiation

    Get PDF
    Rechnerunterstütztes Entwerfen ist eine Disziplin, die in vielen Bereichen des Ingenieurwesens von zunehmender Bedeutung ist. Man bezeichnet diesen Prozess als Computer Aided Design oder bei Schwerpunktlegung auf seine mathematische Seite als Computer Aided Geometric Design und versteht darunter all die Techniken, bei denen Computer zum Entwurf von Produkten Verwendung finden. Diese Produkte (Modelle) basieren auf einer mathematischen Beschreibung der geometrischen Form als Ganzes oder auf diskrete Weise, die es beispielsweise erlaubt, Zeichnungen zu erstellen oder Befehle für numerisch gesteuerte Werkzeugmaschinen zu erzeugen. Ob in der Computergrafik, in der Auswertung von Messdaten oder bei der Funktionsdarstellung, es bedarf dazu der Approximation zumeist komplizierter Funktionen und speziell auch der Interpolation dieser mittels unterschiedlicher einfacherer Ansatzfunktionen. Hier geben wir einen "Überblick" über die Interpolation mittels Polynomen und trigonometrischen Funtionen sowie Splines, wie dies auch in meinem Buch Numerische Mathematik - Vorlesungen, Übungen, Algorithmen und Programme zu finden ist. Natürlich empfiehlt sich bei der praktischen Lösung solcher Aufgaben auch der Einsatz des Computers und von Software. Hier sind einige Rechnungen mit dem Computeralgebrasystem Maple V durchgeführt worden

    Path-Following Method to Determine the Field of Values of a Matrix with High Accuracy

    Get PDF
    We describe a novel and efficient algorithm for calculating the field of values boundary, W()\partial\textrm{W}(\cdot), of an arbitrary complex square matrix: the boundary is described by a system of ordinary differential equations which are solved using Runge--Kutta (Dormand--Prince) numerical integration to obtain control points with derivatives then finally Hermite interpolation is applied to produce a dense output. The algorithm computes W()\partial\textrm{W}(\cdot) both efficiently and with low error. Formal error bounds are proven for specific classes of matrix. Furthermore, we summarise the existing state of the art and make comparisons with the new algorithm. Finally, numerical experiments are performed to quantify the cost-error trade-off between the new algorithm and existing algorithms

    Bilateral approximations of the roots of scalar equations by Lagrange-Aitken-Steffensen method of order three

    Get PDF
    We study the monotone convergence of two general methods of Aitken-Steffenssen type. These methods are obtained from the Lagrange inverse interpolation polynomial of degree two, having controlled nodes. The obtained results provide information on controlling the errors at each iteration step
    corecore