Sökning: "Rational approximation"

Visar resultat 1 - 5 av 19 avhandlingar innehållade orden Rational approximation.

1. 1. Model Order Reduction with Rational Krylov Methods

   Författare :K. Henrik A. Olsson; Axel Ruhe; Volker Mehrmann; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Model order reduction; dual rational Arnoldi; rational Krylov; moment matching; eigenvalue computation; stability analysis; heat exchanger model; Numerical analysis; Numerisk analys;

   Sammanfattning : Rational Krylov methods for model order reduction are studied. A dual rational Arnoldi method for model order reduction and a rational Krylov method for model order reduction and eigenvalue computation have been implemented. It is shown how to deflate redundant or unwanted vectors and how to obtain moment matching. LÄS MER

3. 2. On weak and strong convergence of numerical approximations of stochastic partial differential equations

   Författare :Fredrik Lindgren; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Additive noise; Cahn-Hilliard-Cook equation; Error estimate; Finite element; Hyperbolic equation; Parabolic equation; Rational approximation; Stochastic partial differential equation; Strong convergence; Truncation; Wiener process; Weak convergence; Weak convergence;

   Sammanfattning : This thesis is concerned with numerical approximation of linear stochastic partial differential equations driven by additive noise. In the first part, we develop a framework for the analysis of weak convergence and within this framework we analyze the stochastic heat equation, the stochastic wave equation, and the linearized stochastic Cahn-Hilliard, or the linearized Cahn-Hilliard-Cook equation. LÄS MER

4. 3. Inverse Problems in Analytic Interpolation for Robust Control and Spectral Estimation

   Författare :Johan Karlsson; Anders Lindquist; Alberto Isidori; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Nevanlinna-Pick Interpolation; Approximation; Model Reduction; Robust Control; Gap-robustness; Sensitivity Shaping; Entropy functional; Spectral Estimation; Weak*-topology; Monge-Kantorovic Transportation; Optimization; systems theory; Optimeringslära; systemteori;

   Sammanfattning : This thesis is divided into two parts. The first part deals with theNevanlinna-Pick interpolation problem, a problem which occursnaturally in several applications such as robust control, signalprocessing and circuit theory. We consider the problem of shaping andapproximating solutions to the Nevanlinna-Pick problem in a systematicway. LÄS MER

5. 4. Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and Analysis

   Författare :Andreas Petersson; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Lévy process; Lyapunov equation; white noise; finite element method; multilevel Monte Carlo; Monte Carlo; multiplicative noise; asymptotic mean square stability; stochastic heat equation; covariance operator; weak convergence; generalized Wiener process; numerical approximation; stochastic wave equation; Stochastic partial differential equations;

   Sammanfattning : Stochastic partial differential equations (SPDE) must be approximated in space and time to allow for the simulation of their solutions. In this thesis fully discrete approximations of such equations are considered, with an emphasis on finite element methods combined with rational semigroup approximations. LÄS MER

7. 5. Numerical Approximation of Solutions to Stochastic Partial Differential Equations and Their Moments

   Författare :Kristin Kirchner; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Petrov– Galerkin discretizations; Strong and weak convergence; Fractional operators; Finite element methods; Space-time variational problems; Tensor product spaces; Stochastic partial differential equations; White noise; Petrov– Galerkin discretizations;

   Sammanfattning : The first part of this thesis focusses on the numerical approximation of the first two moments of solutions to parabolic stochastic partial differential equations (SPDEs) with additive or multiplicative noise. More precisely, in Paper I an earlier result (A. Lang, S. Larsson, and Ch. LÄS MER