Sökning: "numerical linear algebra"

Visar resultat 1 - 5 av 13 uppsatser innehållade orden numerical linear algebra.

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 review of the Kaczmarz method

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

   Författare :Carl Lokrantz; [2023]
   Nyckelord :Kaczmarz method; Least squares; Image reconstruction; Iterative method; Linear system of equations; Projection; Numerical Linear Algebra; Block Kaczmarz; Greedy Kaczmarz; Randomized Kaczmarz; Mathematics and Statistics;

   Sammanfattning : The Kaczmarz method is an iterative method for solving linear systems of equations. The Kaczmarz method has been around since it was developed by Kaczmarz 1937. The main idea behind the original Kaczmarz method is to orthogonally project the previous x_k onto the solution space given by a row of the system. LÄS MER

4. 3. Zero Spectrum Subalgebras of K[x] Described by Higher Derivatives

   Kandidat-uppsats, Lunds universitet/Matematik LTH

   Författare :Erik Kennerland; [2023]
   Nyckelord :Algebra; Almost Monomial Subalgebra; Derivation; Lower Degree; Lower Semigroup; Subalgebra Spectrum; Truncation; Mathematics and Statistics;

   Sammanfattning : Unital subalgebras of finite codimension in the polynomial ring $\mathbb{K}[x]$ are described by a finite number of so called subalgebra conditions over a finite set in $\mathbb{K}$ named the subalgebra spectrum. Restricting attention to subalgebras whose spectrum is the singleton $\{0\}$ reveals a rather well behaved class of subalgebras, called almost monomial from the fact that these contain an ideal consisting of all monomials above a certain degree. LÄS MER

5. 4. A Relation Between Anderson Acceleration and GMRES

   Kandidat-uppsats, Lunds universitet/Matematikcentrum

   Författare :Gustaf Lorentzon; [2020]
   Nyckelord :Numerical analysis; acceleration methods; fixed-point iteration; generalized minimal residual method; GMRES; iterative methods; numerical linear algebra; finite difference method; Mathematics and Statistics;

   Sammanfattning : A very common type of problem within mathematics and numerical analysis are fixed-point problems, which can arise as sub-problems of optimization methods, differential equations solvers and much more. The most basic iterative approach for fixed-point problems is fixed-point iteration, special cases of which actually date back as far as the Babylonians, where it was used to to find the square roots of positive numbers. LÄS MER

7. 5. Convergence Rate of the Dirichlet-Neumann Algorithm for Coupled Poisson Equations

   Master-uppsats, Lunds universitet/Matematik LTH

   Författare :Morgan Görtz; [2019]
   Nyckelord :Dirichlet-Neumann; Dirichlet-Neumann algorithm; Poisson equation; convergence rate; finite element method; finite volume method; finite difference method; Mathematics and Statistics;

   Sammanfattning : This thesis presents and tests the convergence rate of the Dirichlet-Neumann algorithm for two Poisson equations coupled by transmission boundary conditions. Three second order discretisation methods are used when analyzing the convergence: standard equidistant finite difference, standard adaptive linear finite element, and standard adaptive finite volume discretisation of Poisson's equation. LÄS MER