Sökning: "Krylov subspaces"

Hittade 4 uppsatser innehållade orden Krylov subspaces.

  1. 1. Randomized Diagonal Estimation

    Master-uppsats, KTH/Matematik (Avd.)

    Författare :Niclas Joshua Popp; [2023]
    Nyckelord :Diagonal estimation; randomized numerical linear algebra; low-rank approximation; matrix functions; Diagonalestimering; randomiserad numerisk linjär algebra; lågrankad approximation; matrisfunktioner;

    Sammanfattning : Implicit diagonal estimation is a long-standing problem that is concerned with approximating the diagonal of a matrix that can only be accessed through matrix-vector products. It is of interest in various fields of application, such as network science, material science and machine learning. LÄS MER

  3. 2. A study of the s-step biconjugate gradient method

    Kandidat-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Författare :Carlotta Boi; [2022]
    Nyckelord :biconjugate gradient methods; s-step biconjugate gradient methods; nonsymmetric linear systems; sparse matrices.; Mathematics and Statistics;

    Sammanfattning : In this thesis we will examine how to solve linear systems using the s-step biconjugate gradient algorithm, which is an iterative method based on the Krylov subspaces. It is useful especially when we have a large and sparse matrix. LÄS MER

  4. 3. Approximating extrema of quadratic forms using Krylov subspaces

    Kandidat-uppsats, Lunds universitet/Matematik LTH

    Författare :Simon Hallborn; [2017]
    Nyckelord :Approximations; Quadratic forms; Krylov subspaces; Eigenvalue problems; Norms; Logarithmic norms; Mathematics and Statistics;

    Sammanfattning : In this thesis approximations to quadratic forms using Krylov subspaces are presented. These quantities are approximations of the norm and logarithmic norm of a matrix. In order to find these quantities an eigenvalue problem has to be solved, but because of limited storage and time, this is not feasible in practice with large matrices. LÄS MER

  5. 4. GMRES and Weighted GMRES for solving nonsymmetric linear systems

    Kandidat-uppsats, Lunds universitet/Matematik LTH

    Författare :Gustav Kratz; [2016]
    Nyckelord :Nonsymmetric linear systems; Krylov subspaces; Iterative methods; Arnoldi; GMRES; Mathematics and Statistics;

    Sammanfattning : The Implementation and some mathematical properties of GMRES and weighted GMRES (WGMRES) are described. Numerical experiments originally performed by Essai (1998) are performed to compare the two methods. GMRES and WGMRES are used to solve a linear system arising from the Poisson equation and compared with respect to computational effort.. LÄS MER