Essays about: "Orthonormal basis"

Showing result 1 - 5 of 6 essays containing the words Orthonormal basis.

  1. 1. A Mathematical Analysis of the Harmonic Oscillator in Quantum Mechanics

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Philip Solarz; [2021]
    Keywords : Functional Analysis; Quantum Mechanics; Harmonic Oscillator; Schrödinger Equation; Hamiltonian Operator; Hermite Functions; Hilbert Space; Schatten-von Neumann Operator; Mehler s Formula;

    Abstract : In this paper we derive the eigenfunctions to the Hamiltonian operator associated with the Harmonic Oscillator, and show that they are given by the Hermite functions. Then we prove that the Hermite functions form an orthonormal basis in the underlying Hilbert space. READ MORE

  3. 2. Comparative Study of Several Bases in Functional Analysis

    University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

    Author : Maria Miranda Navarro; [2018]
    Keywords : Banach space; Hilbert space; Hamel basis; Schauder basis; Orthonormal basis;

    Abstract : From the beginning of the study of spaces in functional analysis, bases have been an indispensable tool for operating with vectors and functions over a concrete space. Bases can be organized by types, depending on their properties. This thesis is intended to give an overview of some bases and their relations. READ MORE

  4. 3. System Identification by Adaptive Boosting

    University essay from KTH/Reglerteknik

    Author : Johan Bjurgert; [2015]
    Keywords : ;

    Abstract : In the field of machine learning, the algorithm Adaptive Boosting has beensuccessfully applied to a wide range of regression and classification problems.Still, there is no known method to use the algorithm to estimate dynamical systems.In this thesis, the relationship between Adaptive Boosting and systemidentification is explored. READ MORE

  5. 4. Numerical Implementations of the Generalized Minimal Residual Method (GMRES)

    University essay from Lunds universitet/Matematik LTH

    Author : Ivo Dravins; [2015]
    Keywords : Generalized Minimal Residual Method; Jacobian-free; GMRES; Householder; Givens rotations; Gram-Schmidt; Mathematics and Statistics;

    Abstract : The generalized minimal residual method (GMRES) is an iterative method used to find numerical solutions to non-symmetric linear systems of equations. The method relies on constructing an orthonormal basis of the Krylov space and is thus vulnerable to an imperfect basis caused by computational errors. READ MORE

  6. 5. Image Compression by Using Haar Wavelet Transform and Singualr Value Decomposition

    University essay from Institutionen för datavetenskap, fysik och matematik, DFM

    Author : Zunera Idrees; Eliza Hashemiaghjekandi; [2011]
    Keywords : Multi resolution analysis; Haar wavelet transformation MRA ; Average and difference method; Singular value decomposition SVD .;

    Abstract : The rise in digital technology has also rose the use of digital images. The digital imagesrequire much storage space. The compression techniques are used to compress the dataso that it takes up less storage space. In this regard wavelets play important role. READ MORE