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Haar wavelets method for solving Pocklington's integral equation

M. Shamsi, Mohsen Razzaghi, J. Nazarzadeh, Masoud Shafiee (2004)

Kybernetika

A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington’s integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington’s integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic equations. Through numerical examples, performance of the present method is investigated concerning the...

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....

Identification of basic thermal technical characteristics of building materials

Stanislav Šťastník, Jiří Vala, Hana Kmínová (2007)

Kybernetika

Modelling of building heat transfer needs two basic material characteristics: heat conduction factor and thermal capacity. Under some simplifications these two factors can be determined from a rather simple equipment, generating heat from one of two aluminium plates into the material sample and recording temperature on the contacts between the sample and the plates. However, the numerical evaluation of both characteristics leads to a non-trivial optimization problem. This article suggests an efficient...

Indefinite integration of oscillatory functions

Paweł Keller (1998)

Applicationes Mathematicae

A simple and fast algorithm is presented for evaluating the indefinite integral of an oscillatory function ∫ x y i f ( t ) e i ω t d t , -1 ≤ x < y ≤ 1, ω ≠ 0, where the Chebyshev series expansion of the function f is known. The final solution, expressed as a finite Chebyshev series, is obtained by solving a second-order linear difference equation. Because of the nature of the equation special algorithms have to be used to find a satisfactory approximation to the integral.

Linear transforms supporting circular convolution over a commutative ring with identity

Mohamed Mounir Nessibi (1995)

Commentationes Mathematicae Universitatis Carolinae

We consider a commutative ring R with identity and a positive integer N . We characterize all the 3-tuples ( L 1 , L 2 , L 3 ) of linear transforms over R N , having the “circular convolution” property, i.eṡuch that x * y = L 3 ( L 1 ( x ) ⊗ L 2 ( y ) ) for all x , y ∈ R N .

Linear-wavelet networks

Roberto Galvão, Victor Becerra, João Calado, Pedro Silva (2004)

International Journal of Applied Mathematics and Computer Science

This paper proposes a nonlinear regression structure comprising a wavelet network and a linear term. The introduction of the linear term is aimed at providing a more parsimonious interpolation in high-dimensional spaces when the modelling samples are sparse. A constructive procedure for building such structures, termed linear-wavelet networks, is described. For illustration, the proposed procedure is employed in the framework of dynamic system identification. In an example involving a simulated...

Currently displaying 81 – 100 of 186