Sökning: "conjugate gradients"

Visar resultat 1 - 5 av 9 avhandlingar innehållade orden conjugate gradients.

  1. 1. Parallelizing the Method of Conjugate Gradients for Shared Memory Architectures

    Författare :Henrik Löf; Jarmo Rantakokko; Erik Hagersten; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Beräkningsvetenskap; Scientific Computing;

    Sammanfattning : Solving Partial Differential Equations (PDEs) is an important problem in many fields of science and engineering. For most real-world problems modeled by PDEs, we can only approximate the solution using numerical methods. Many of these numerical methods result in very large systems of linear equations. LÄS MER

  3. 2. Iterative and Adaptive PDE Solvers for Shared Memory Architectures

    Författare :Henrik Löf; Jarmo Rantakokko; Sverker Holmgren; Erik Hagersten; Mark Bull; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; partial differential equations; iterative methods; finite elements; conjugate gradients; adaptive mesh refinement; multigrid; cc-NUMA; distributed shared memory; OpenMP; page migration; TLB shoot-down; bandwidth minimization; reverse Cuthill-McKee; migrate-on-next-touch; affinity; temporal locality; chip multiprocessors; CMP; Beräkningsvetenskap; Scientific Computing;

    Sammanfattning : Scientific computing is used frequently in an increasing number of disciplines to accelerate scientific discovery. Many such computing problems involve the numerical solution of partial differential equations (PDE). LÄS MER

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

    Författare :Tove Odland; Anders Forsgren; William W. Hager; KTH; []
    Nyckelord :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;

    Sammanfattning : 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. LÄS MER

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

    Författare :David Ek; Anders Forsgren; Jacek Gondzio; KTH; []
    Nyckelord :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;

    Sammanfattning : 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. LÄS MER

  7. 5. Some Mathematical Aspects of Thermo and Fluid Dynamics

    Författare :Carl Fredrik Stein; Göteborgs universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; swirling jets; vortex breakdown; conical self-similarity; Long s jet; Taylor s hypothesis; frozen turbulence hypothesis; advection velocity; conjugate heat transfer; asymptotic analysis; swirling jets;

    Sammanfattning : This thesis contains mathematical treatments of three issues in thermo and fluid dynamics: swirling jets and vortex breakdown, Taylor's hypothesis and conjugate heat transfer. The work on swirling jets is focused on the study of the well-posedness of the conically self-similar free-vortex solutions to the Navier--Stokes equations. LÄS MER