Search for dissertations about: "quadratic equations"

Showing result 1 - 5 of 45 swedish dissertations containing the words quadratic equations.

  1. 1. On Methods for Solving Symmetric Systems of Linear Equations Arising in Optimization

    Author : Tove Odland; Anders Forsgren; William W. Hager; KTH; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; symmetric system of linear equations; method of conjugate gradients; quasi-Newton method; unconstrained optimization; unconstrained quadratic optimiza- tion; Krylov subspace method; unnormalized Lanczos vectors; minimum-residual method; symmetriska linjära ekvationssystem; konjugerade gradientmetoden; kvasi- Newtonmetoder; optimering utan bivillkor; kvadratisk optimering utan bivillkor; Kry- lovunderrumsmetoder; icke-normaliserade Lanczosvektorer; minimum-residualmetoden; Mathematics; Matematik;

    Abstract : In this thesis we present research on mathematical properties of methods for solv- ing symmetric systems of linear equations that arise in various optimization problem formulations and in methods for solving such problems.In the first and third paper (Paper A and Paper C), we consider the connection be- tween the method of conjugate gradients and quasi-Newton methods on strictly convex quadratic optimization problems or equivalently on a symmetric system of linear equa- tions with a positive definite matrix. READ MORE

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

    Author : Andreas Petersson; Chalmers University of Technology; []
    Keywords : 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;

    Abstract : 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. READ MORE

  3. 3. Mathematics textbooks for teaching : An analysis of content knowledge and pedagogical content knowledge concerning algebra in Swedish upper secondary education

    Author : Wang Wei Sönnerhed; Berner Lindström; Jonas Emanuelsson; Ingemar Holgersson; Göteborgs universitet kommunikation och lärande Institutionen för pedagogik; []
    Keywords : mathematics textbooks; school algebra; solving methods; factorization; solving quadratic equations; mathematics teaching; content knowledge; pedagogical content knowledge; geometrical models; algebra history; embedded teaching trajectories;

    Abstract : In school algebra, using different methods including factorization to solve quadratic equations is one common teaching and learning topic at upper secondary school level. This study is about analyzing the algebra content related to solving quadratic equations and the method of factorization as presented in Swedish mathematics textbooks with subject matter content knowledge (CK) and pedagogical content knowledge (PCK) as analytical tools. READ MORE

  4. 4. Approaches to accelerate methods for solving systems of equations arising in nonlinear optimization

    Author : David Ek; Anders Forsgren; Jacek Gondzio; KTH; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Nonlinear optimization; mathematical programming; interior-point methods; approximate solutions to systems of linear equations; method of conjugate gradients; quasi-Newton methods; modified Newton methods; Ickelinjär optimering; matematisk programmering; inre-punktsmetoder; approximativa lösningar till linjära ekvationssystem; konjugerade gradientmetoden; kvasi-Newtonmetoder; modifierade Newtonmetoder.; Optimeringslära och systemteori; Optimization and Systems Theory;

    Abstract : Methods for solving nonlinear optimization problems typically involve solving systems of equations. This thesis concerns approaches for accelerating some of those methods. In our setting, accelerating involves finding a trade-off between the computational cost of an iteration and the quality of the computed search direction. READ MORE

  5. 5. Symplectic methods for isospectral flows and 2D ideal hydrodynamics

    Author : Milo Viviani; Chalmers University of Technology; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Structure preserving algorithms; Symplectic methods; Isospectral flows; Integrability theory; Fluid dynamics; Geometric integration; Lie--Possion systems; Hamiltonian systems; Euler equations;

    Abstract : The numerical solution of non-canonical Hamiltonian systems is an active and still growing field of research. At the present time, the biggest challenges concern the realization of structure preserving algorithms for differential equations on infinite dimensional manifolds. READ MORE