Essays about: "Toeplitz matrices"

Showing result 1 - 5 of 6 essays containing the words Toeplitz matrices.

  1. 1. A geometric approach to calculating the limit set of eigenvalues for banded Toeplitz matrices

    University essay from Lunds universitet/Matematik LTH

    Author : Teodor Bucht; [2023]
    Keywords : Toeplitz matrices; Banded Toeplitz matrices; Limit set; Eigenvalues; Mathematics and Statistics;

    Abstract : This thesis is about the limiting eigenvalue distribution of n × n Toeplitz matrices as n → ∞. The two classical questions we want to answer are: what is the limit set of the eigenvalues, and what is the limiting distribution of the eigenvalues. Our main result is a new approach to calculate the limit set Λ(b) for a Laurent polynomial b, i.e. READ MORE

  3. 2. Exploring and extending eigensolvers for Toeplitz(-like) matrices : A study of numerical eigenvalue and eigenvector computations combined with matrix-less methods

    University essay from Uppsala universitet/Institutionen för informationsteknologi

    Author : Martin Knebel; Fredrik Cers; Oliver Groth; [2022]
    Keywords : Toeplitz matrices; eigenvalue computation; eigenvector computation; matrix-less methods;

    Abstract : We implement an eigenvalue solving algorithm proposed by Ng and Trench, specialized for Toeplitz(-like) matrices, utilizing root finding in conjunction with an iteratively calculated version of the characteristic polynomial. The solver also yields corresponding eigenvectors as a free bi-product. READ MORE

  4. 3. A Matrix-less Method for Approximating the Eigenvectors of Toeplitz-like Matrices

    University essay from Uppsala universitet/Institutionen för informationsteknologi

    Author : David Meadon; [2021]
    Keywords : ;

    Abstract : Matrix-less methods (MLM) have successfully been used to efficiently approximate the eigenvalues of certain classes of structured matrices. Specifically, the method has been used to approximate the eigenvalues of Toeplitz and Toeplitz-like matrices. READ MORE

  5. 4. Optimizing multigrid smoothers using GLT theory

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematikcentrum

    Author : Denhanh Huynh; [2020]
    Keywords : multigrid; smoothers; GLT; Mathematics and Statistics;

    Abstract : Multigrid algorithms are algorithms used to find numerical solutions to differential equations using a hierarchy of grids of different coarseness. This exploits the fact that short-wavelength components of the solutions converges at a faster rate than the long-wavelength components when using some basic iterative methods, such as the Jacobi method or the Gauss-Seidel method. READ MORE

  6. 5. Limiting Behavior of the Largest Eigenvalues of Random Toeplitz Matrices

    University essay from KTH/Matematik (Inst.)

    Author : Samuel Modée; [2019]
    Keywords : Random matrix; Toeplitz matrix; largest eigenvalues; eigenvectors; slumpmatriser; Toeplitz matrices; största egenvärde; egenvektorer;

    Abstract : We consider random symmetric Toeplitz matrices of size n. Assuming that the entries on the diagonals are independent centered random variables with finite γ-th moment (γ>2), a law of large numbers is established for the largest eigenvalue. READ MORE