Essays about: "Chebyshev function"

Showing result 1 - 5 of 10 essays containing the words Chebyshev function.

  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. The Riemann Zeta Function and Prime Numbers

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Oskar Rune; Linus Envall; [2023]
    Keywords : ;

    Abstract : This thesis is the result of a literature study regarding the relationship between the Riemann zeta function and prime numbers. We introduce the $\zeta$ function, discussing its properties. Then, starting from Riemann's original series, we derive the Euler product formula and functional equation for $\zeta$. READ MORE

  4. 3. An operator theoretic approach to the Riemann Hypothesis

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Ramon Arjan van de Scheur; [2023]
    Keywords : Riemann hypothesis; Prime number theorem; Prime number theorem for arithmetic progressions; operator theoretic equivalent; compact operator; prime-counting function; Chebyshev function; Laplace transform; Fourier transform; convolution operator; weak topology; strong topology; compact perturbation; Tauberian theorem; Poisson kernel; holomorphic; self-adjoint; spectrum; trace; Mathematics and Statistics;

    Abstract : In 2023 an operator theoretic approach to the Prime Number Theorem was introduced by Olsen. In this thesis this approach is examined and applied to give a new, operator theoretic, proof of a different version of the Prime Number Theorem and of the Prime Number Theorem for arithmetic progressions. READ MORE

  5. 4. Relating the Arnoldi approximation to the best Chebyshev approximation of the characteristic polynomial - A study using a complex valued variant of the Remez algorithm

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Thomas Renström; [2022]
    Keywords : Chebyshev; Arnoldi; Remez; Tang; approximation; matrix; complex; characteristic polynomial; Mathematics and Statistics;

    Abstract : The Remez algorithm is a beautiful algorithm that finds the best approximation to a function by finding points satisfying the alternation condition. In 1987 Ping Tang published his doctoral thesis detailing a version of the Remez algorithm modified for functions of complex values with complex coefficients. READ MORE

  6. 5. 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