Essays about: "polynomial matrix"
Showing result 1 - 5 of 18 essays containing the words polynomial matrix.
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1. A C++ Matrix library for computing the Gateaux derivative of the Fermi-Dirac operator
University essay from Uppsala universitet/Avdelningen för beräkningsvetenskapAbstract : 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. READ MORE
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2. Randomized Diagonal Estimation
University essay from KTH/Matematik (Avd.)Abstract : 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. READ MORE
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3. Zero Spectrum Subalgebras of K[x] Described by Higher Derivatives
University essay from Lunds universitet/Matematik LTHAbstract : 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. READ MORE
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4. Relating the Arnoldi approximation to the best Chebyshev approximation of the characteristic polynomial - A study using a complex valued variant of the Remez algorithm
University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/MatematikcentrumAbstract : The Remez algorithm is a beautiful algorithm that finds the best approximation to a function by finding points satisfying the alternation condition. In 1987 Ping Tang published his doctoral thesis detailing a version of the Remez algorithm modified for functions of complex values with complex coefficients. READ MORE
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5. 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 informationsteknologiAbstract : 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
