Essays about: "Chebyshev interpolation"

Found 4 essays containing the words Chebyshev interpolation.

  1. 1. Data-driven Interpolation Methods Applied to Antenna System Responses : Implementation of and Benchmarking

    University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)

    Author : Lucas Åkerstedt; [2023]
    Keywords : Model Order Reduction; Loewner Framework; State-space Representation; Nevanlinna-Pick Interpolation; Vector Fitting; Cauchy interpolation; Antenna System Responses; Benchmarking; MoM; Data-driven; Interpolation; Modelordningsreducering; Loewner Ramverk; Tillståndsrepresentation; NevanlinnaPick Interpolering; Vector Fitting; Cauchy Interpolering; Antennsystemsvar; Prestandajämförelse; MoM; Datadriven; Interpolering;

    Abstract : With the advances in the telecommunications industry, there is a need to solve the in-band full-duplex (IBFD) problem for antenna systems. One premise for solving the IBFD problem is to have strong isolation between transmitter and receiver antennas in an antenna system. READ MORE

  3. 2. Comparing trigonometric interpolation against the Barycentric form of Lagrange interpolation : A battle of accuracy, stability and cost

    University essay from Linköpings universitet/Tillämpad matematik; Linköpings universitet/Tekniska fakulteten

    Author : Beatrice Söderqvist; [2022]
    Keywords : Interpolation; Big O-notation; Cardinal function; Lagrange Interpolation; Barycentric Lagrange Interpolation; Trigonometric Interpolation; Parametrization;

    Abstract : This report analyzes and compares Barycentric Lagrange interpolation to Cardinal Trigonometric interpolation, with regards to computational cost and accuracy. It also covers some edge case scenarios which may interfere with the accuracy and stability. READ MORE

  4. 3. Optimising the Choice of Interpolation Nodes with a Forbidden Region

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Felix Bengtsson; Alex Hamben; [2022]
    Keywords : Interpolation; Chebyshev; polynomial interpolation; Lebesgue Constant; optimization; numerical methods;

    Abstract : We consider the problem of optimizing the choice of interpolation nodes such that the interpolation error is minimized, given the constraint that none of the nodes may be placed inside a forbidden region. Restricting the problem to using one-dimensional polynomial interpolants, we explore different ways of quantifying the interpolation error; such as the integral of the absolute/squared difference between the interpolated function and the interpolant, or the Lebesgue constant, which compares the interpolant with the best possible approximating polynomial of a given degree. READ MORE

  5. 4. Feigenbaum Scaling

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Janek Sendrowski; [2020]
    Keywords : Feigenbaum; Feigenbaum constant; Feigenbaum point; superstable; self-similarity; fractals; final-state diagram; logistic map; period-doubling operator; linearized period-doubling operator; Cantor set; Sharkovsky sequence; Chebyshev interpolation; stable manifold; unstable manifold; orbits; fixed points; scaling factor; pitchfork bifurcation; cobweb plot; renormalization; iterates; one-hump map; unimodal map; bifurcation cascade; Feigenbaum universality; chaos theory; spectrum; generalized Feigenvalues; bifurcation points; superstable points; fixed function; universal function; eigenvalues; eigenvectors; eigenfunctions; universality conditions; Schwarzian derivative; Newton’s method; power method; Arnoldi’s method; attractive fixed point; repellent fixed point; Banach fixed-point theorem; collocation method; functional analysis; topology;

    Abstract : In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. READ MORE