Search for dissertations about: "solving quadratic equations"

Showing result 1 - 5 of 17 swedish dissertations containing the words solving quadratic equations.

  2. 1. 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. 2. On Methods for Solving Symmetric Systems of Linear Equations Arising in Optimization

    Author : Tove Odland; Anders Forsgren; William W. Hager; KTH; []
    Keywords : 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

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

    Author : David Ek; Anders Forsgren; Jacek Gondzio; KTH; []
    Keywords : 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.; Optimization and Systems Theory; Optimeringslära och systemteori;

    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

  6. 4. Tools for Control System Design : Stratification of Matrix Pairs and Periodic Riccati Differential Equation Solvers

    Author : Stefan Johansson; Bo Kågström; Erik Elmroth; Paul Van Dooren; Umeå universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; control system design; stratification; controllability; observability; matrix pair; canonical forms; linear quadratic regulator; periodic systems; periodic Riccati differential equation; Computer science; Datavetenskap; Numerical Analysis; numerisk analys;

    Abstract : Modern control theory is today an interdisciplinary area of research. Just as much as this can be problematic, it also provides a rich research environment where practice and theory meet. This Thesis is conducted in the borderline between computing science (numerical analysis) and applied control theory. READ MORE

  7. 5. Adjoint-based aerodynamic shape optimization

    Author : Olivier Amoignon; Martin Berggren; Uppsala universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Numerical Analysis; Numerisk analys;

    Abstract : An adjoint system of the Euler equations of gas dynamics is derived in order to solve aerodynamic shape optimization problems with gradient-based methods. The derivation is based on the fully discrete flow model and involves differentiation and transposition of the system of equations obtained by an unstructured and node-centered finite-volume discretization. READ MORE