Essays about: "Arnoldi"

Showing result 1 - 5 of 6 essays containing the word Arnoldi.

  1. 1. 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

  3. 2. Risk Measurement and Performance Attribution for IRS Portfolios Using a Generalized Optimization Method for Term Structure Estimation

    University essay from Linköpings universitet/Produktionsekonomi

    Author : Fredrik Gerdin Börjesson; Christoffer Eduards; [2021]
    Keywords : Interest rate measurement; term structures; multiple yield curves; principal component analysis; systematic risk; risk factors; term structure simulation; Latin hypercube sampling with dependence; risk measurement; value-at-risk; expected shortfall; interest rate swap; performance attribution;

    Abstract : With the substantial size of the interest rate markets, the importance of accurate pricing, risk measurement and performance attribution can not be understated. However, the models used on the markets often have underlying issues with capturing the market's fundamental behavior. READ MORE

  4. 3. An Overview of Rosenbrock-Krylov Methods for the Numerical Solution of Ordinary Differential Equations

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

    Author : Jens Axelsson; [2021]
    Keywords : Rosenbrock-Krylov methods; Rosenbrock methods; Krylov subspace methods; stiff ODEs; Mathematics and Statistics;

    Abstract : This thesis offers an overview of the relatively new family of Rosenbrock-Krylov numerical methods for ODEs. These methods are a further development of Rosenbrock methods, using a lower-dimension approximation of the Jacobian. 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

  6. 5. Computation of Eigenmodes in Three-Dimensional Structures

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Daniel Lilja; Olof Hummelgren; [2020]
    Keywords : ;

    Abstract : In this thesis the eigenmodes and eigenvalues of three dimensional structures are analyzed using the Python environment FEniCS in combination with an implementation of the Arnoldi method in MATLAB for calculation of eigenpairs. This is done by considering separable solutions of the wave equation and subsequently expressing these as the solutions to an eigenvalue problem. READ MORE