Search for dissertations about: "Krylov methods"

Showing result 1 - 5 of 23 swedish dissertations containing the words Krylov methods.

  2. 1. Numerical methods for Sylvester-type matrix equations and nonlinear eigenvalue problems

    Author : Emil Ringh; Elias Jarlebring; Johan Karlsson; Per Enqvist; Daniel Kressner; KTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Matrix equations; Lyapunov equation; Sylvester equation; nonlinear eigenvalue problems; two-parameter eigenvalue problems; Krylov methods; iterative methods; preconditioning; projection methods; Matrisekvationer; Lyapunovekvationen; Sylvesterekvationen; ickelinjära egenvärdesproblem; två-parameters egenvärdesproblem; Krylovmetoder; iterativa metoder; förkonditionering; projektionsmetoder; Tillämpad matematik och beräkningsmatematik; Applied and Computational Mathematics; Optimization and Systems Theory; Optimeringslära och systemteori; Numerical Analysis; Numerisk analys;

    Abstract : Linear matrix equations and nonlinear eigenvalue problems (NEP) appear in a wide variety of applications in science and engineering. Important special cases of the former are the Lyapunov equation, the Sylvester equation, and their respective generalizations. These appear, e.g. READ MORE

  4. 2. Numerical Methods for Wave Propagation : Analysis and Applications in Quantum Dynamics

    Author : Emil Kieri; Sverker Holmgren; Vasile Gradinaru; Hans O. Karlsson; Tobias Jahnke; Uppsala universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; computational wave propagation; quantum dynamics; time-dependent Schrödinger equation; spectral methods; Gaussian beams; splitting methods; low-rank approximation; Scientific Computing; Beräkningsvetenskap;

    Abstract : We study numerical methods for time-dependent partial differential equations describing wave propagation, primarily applied to problems in quantum dynamics governed by the time-dependent Schrödinger equation (TDSE). We consider both methods for spatial approximation and for time stepping. READ MORE

  5. 3. Numerical methods for parameterized linear systems

    Author : Siobhán Correnty; Elias Jarlebring; Johan Karlsson; Kirk M. Soodhalter; Andrew J. Wathen; KTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Parameterized linear systems; Krylov subspace methods; preconditioning; tensor decompositions; shifted linear systems; parameterized partial differential equations; time-delay systems; transfer functions; parameter estimation problems; Parameteriserade linjära system; Krylov-metoder; förkonditionering; tensordekomposition; skiftade linjära system; parametriserade partiella differentialekvationer; tidsfördröjningssystem; överföringsfunktioner; parameteruppskattningsproblem; Numerical Analysis; Numerisk analys;

    Abstract : Solving linear systems of equations is a fundamental problem in engineering. Moreover, applications involving the solution to linear systems arise in the social sciences, business, and economics. Specifically, the research conducted in this dissertation explores solutions to linear systems where the system matrix depends nonlinearly on a parameter. READ MORE

  6. 4. Model Order Reduction with Rational Krylov Methods

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

    Abstract : 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. READ MORE

  7. 5. Krylov Subspace Methods for Linear Systems, Eigenvalues and Model Order Reduction

    Author : Daniel Skoogh; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; eigenvalues; eigenvectors; sparse; parallel; rational; Krylov; shift; invert; Arnoldi; linear systems; iterative; model; reduction; passive; 65F15; 65F50; 65Y05; 65F10; 93A30; 93B40; rational;

    Abstract : New variants of Krylov subspace methods for numerical solution of linear systems, eigenvalue, and model order reduction problems are described. A new method to solve linear systems of equations with several right-hand sides is described. READ MORE