Sökning: "polynomial matrices"

Visar resultat 1 - 5 av 12 uppsatser innehållade orden polynomial matrices.

  1. 1. A C++ Matrix library for computing the Gateaux derivative of the Fermi-Dirac operator

    Kandidat-uppsats, Uppsala universitet/Avdelningen för beräkningsvetenskap

    Författare :William Samuelsson; [2023]
    Nyckelord :C ; Quantum Chemistry; Matrix functions;

    Sammanfattning : Computing the Fermi-Dirac operator is done through recursive polynomial expansions, using the SP2 and SP2 Acc algorithms. The Gateaux derivative is computed for both schemes by mapping the zeroth and first order matrices onto a block upper triangular matrix, which is implemented in Python using Numpy arrays to store full matrices and in C++ by first constructing a basic matrix library to use as blocks in a later created block upper triangular matrix library which only directly references two blocks in a 2 x 2 block matrix. LÄS MER

  3. 2. 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

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

    Master-uppsats, Lunds universitet/Matematik LTH

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

    Sammanfattning : 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. LÄS MER

  5. 4. De-quantizing quantum machine learning algorithms

    Master-uppsats, Linköpings universitet/Informationskodning

    Författare :Stefanie Sköldhed; [2022]
    Nyckelord :Quantum Machine Learning Algorithm; Classical Machine Learning Algorithm; Speedup; Recommendation Systems;

    Sammanfattning : Today, a modern and interesting research area is machine learning. Another new and exciting research area is quantum computation, which is the study of the information processing tasks accomplished by practising quantum mechanical systems. This master thesis will combine both areas, and investigate quantum machine learning. LÄS MER

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

    Kandidat-uppsats, Uppsala universitet/Institutionen för informationsteknologi

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

    Sammanfattning : 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. LÄS MER