Sökning: "Interval arithmetic"

Hittade 5 avhandlingar innehållade orden Interval arithmetic.

  1. 1. Computational dynamics – real and complex

    Författare :Anna Belova; Warwick Tucker; Denis Gaidashev; Àlex Haro Provinciale; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Continued fractions; Generating functions; Rotation numbers; Rigorous computations; Interval analysis; Interval arithmetic; Multipliers; Quadratic map; Kuramoto-Sivashinsky equation; Mathematics; Matematik;

    Sammanfattning : The PhD thesis considers four topics in dynamical systems and is based on one paper and three manuscripts.In Paper I we apply methods of interval analysis in order to compute the rigorous enclosure of rotation number. LÄS MER

  3. 2. A Numerical Study of the Lorenz and Lorenz-Stenflo Systems

    Författare :Tommy Ekola; Michael Benedicks; Robert MacKay; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Warwick Tucker; Strange attractor; Lorenz equations; Lorenz-Stenflo equations; Lorenz attractor; Lorenz-Stenflo attractor; Dynamical systems; Normal form theory; MATEMATIK; MATHEMATICS; MATEMATIK;

    Sammanfattning : In 1998 the Swedish mathematician Warwick Tucker used rigorous interval arithmetic and normal form theory to prove the existence of a strange attractor in the Lorenz system. In large parts, that proof consists of computations implemented and performed on a computer. LÄS MER

  4. 3. Path-planning with obstacle-avoiding minimum curvature variation B-splines

    Författare :Tomas Berglund; Luleå tekniska universitet; []
    Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; Industriell elektronik; Industrial Electronics;

    Sammanfattning : We study the general problem of computing an obstacle-avoiding path that, for a prescribed weight, minimizes the weighted sum of a smoothness measure and a safety measure of the path. We consider planar curvature-continuous paths, that are functions on an interval of a room axis, for a point-size vehicle amidst obstacles. LÄS MER

  5. 4. Numerical analysis for random processes and fields and related design problems

    Författare :Konrad Abramowicz; Oleg Seleznjev; Krzysztof Podgórski; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; stochastic processes; random fields; approximation; numerical integration; Hermite splines; piecewise linear interpolator; local stationarity; point singularity; stratified Monte Carlo quadrature; Asian option; Monte Carlo pricing method; Lévy market models; Mathematical statistics; Matematisk statistik; Mathematical Statistics; matematisk statistik;

    Sammanfattning : In this thesis, we study numerical analysis for random processes and fields. We investigate the behavior of the approximation accuracy for specific linear methods based on a finite number of observations. Furthermore, we propose techniques for optimizing performance of the methods for particular classes of random functions. LÄS MER

  7. 5. Hierarchical Variance Reduction Techniques for Monte Carlo Rendering

    Författare :Petrik Clarberg; Institutionen för datavetenskap; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; computer graphics; Monte Carlo methods; importance sampling; hierarchical techniques; rendering;

    Sammanfattning : Ever since the first three-dimensional computer graphics appeared half a century ago, the goal has been to model and simulate how light interacts with materials and objects to form an image. The ultimate goal is photorealistic rendering, where the created images reach a level of accuracy that makes them indistinguishable from photographs of the real world. LÄS MER