Optimization of the prediction of second refined wavelet coefficients in electron structure calculations

Brigita Sziová, Szilvia Nagy, János Pipek

Research output: Contribution to journalArticle

Abstract

In wavelet-based solution of eigenvalue-type differential equations, like the Schrödinger equation, refinement in the resolution of the solution is a costly task, as the number of the potential coefficients in the wavelet expansion of the solution increases exponentially with the resolution. Predicting the magnitude of the next resolution level coefficients from an already existing solution in an economic way helps to either refine the solution,or to select the coefficients, which are to be included into the next resolution level calculations, or to estimate the magnitude of the error of the solution. However, after accepting a solution with a predicted refinement as a basis, the error can still be estimated by a second prediction, i.e., from a prediction to the second finer resolution level coefficients. These secondary predicted coefficients are proven to be oscillating around the values of the wavelet expansion coefficients of the exact solution. The optimal averaging of these coefficients is presented in the following paper using a sliding average with three optimized coefficients for simple, one-dimensional electron structures.

Original languageEnglish
Pages (from-to)643-650
Number of pages8
JournalOpen Physics
Volume14
Issue number1
DOIs
Publication statusPublished - Jan 1 2016

Fingerprint

optimization
coefficients
predictions
electrons
expansion
sliding
economics
differential equations
eigenvalues
estimates

Keywords

  • Prediction of refinement
  • Schrödinger equation
  • Variation
  • Wavelet analysis

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Optimization of the prediction of second refined wavelet coefficients in electron structure calculations. / Sziová, Brigita; Nagy, Szilvia; Pipek, János.

In: Open Physics, Vol. 14, No. 1, 01.01.2016, p. 643-650.

Research output: Contribution to journalArticle

@article{724e1634038249ccb9a63e9d5779086a,
title = "Optimization of the prediction of second refined wavelet coefficients in electron structure calculations",
abstract = "In wavelet-based solution of eigenvalue-type differential equations, like the Schr{\"o}dinger equation, refinement in the resolution of the solution is a costly task, as the number of the potential coefficients in the wavelet expansion of the solution increases exponentially with the resolution. Predicting the magnitude of the next resolution level coefficients from an already existing solution in an economic way helps to either refine the solution,or to select the coefficients, which are to be included into the next resolution level calculations, or to estimate the magnitude of the error of the solution. However, after accepting a solution with a predicted refinement as a basis, the error can still be estimated by a second prediction, i.e., from a prediction to the second finer resolution level coefficients. These secondary predicted coefficients are proven to be oscillating around the values of the wavelet expansion coefficients of the exact solution. The optimal averaging of these coefficients is presented in the following paper using a sliding average with three optimized coefficients for simple, one-dimensional electron structures.",
keywords = "Prediction of refinement, Schr{\"o}dinger equation, Variation, Wavelet analysis",
author = "Brigita Sziov{\'a} and Szilvia Nagy and J{\'a}nos Pipek",
year = "2016",
month = "1",
day = "1",
doi = "10.1515/phys-2016-0063",
language = "English",
volume = "14",
pages = "643--650",
journal = "Open Physics",
issn = "1895-1082",
publisher = "Walter de Gruyter GmbH & Co. KG",
number = "1",

}

TY - JOUR

T1 - Optimization of the prediction of second refined wavelet coefficients in electron structure calculations

AU - Sziová, Brigita

AU - Nagy, Szilvia

AU - Pipek, János

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In wavelet-based solution of eigenvalue-type differential equations, like the Schrödinger equation, refinement in the resolution of the solution is a costly task, as the number of the potential coefficients in the wavelet expansion of the solution increases exponentially with the resolution. Predicting the magnitude of the next resolution level coefficients from an already existing solution in an economic way helps to either refine the solution,or to select the coefficients, which are to be included into the next resolution level calculations, or to estimate the magnitude of the error of the solution. However, after accepting a solution with a predicted refinement as a basis, the error can still be estimated by a second prediction, i.e., from a prediction to the second finer resolution level coefficients. These secondary predicted coefficients are proven to be oscillating around the values of the wavelet expansion coefficients of the exact solution. The optimal averaging of these coefficients is presented in the following paper using a sliding average with three optimized coefficients for simple, one-dimensional electron structures.

AB - In wavelet-based solution of eigenvalue-type differential equations, like the Schrödinger equation, refinement in the resolution of the solution is a costly task, as the number of the potential coefficients in the wavelet expansion of the solution increases exponentially with the resolution. Predicting the magnitude of the next resolution level coefficients from an already existing solution in an economic way helps to either refine the solution,or to select the coefficients, which are to be included into the next resolution level calculations, or to estimate the magnitude of the error of the solution. However, after accepting a solution with a predicted refinement as a basis, the error can still be estimated by a second prediction, i.e., from a prediction to the second finer resolution level coefficients. These secondary predicted coefficients are proven to be oscillating around the values of the wavelet expansion coefficients of the exact solution. The optimal averaging of these coefficients is presented in the following paper using a sliding average with three optimized coefficients for simple, one-dimensional electron structures.

KW - Prediction of refinement

KW - Schrödinger equation

KW - Variation

KW - Wavelet analysis

UR - http://www.scopus.com/inward/record.url?scp=85014670153&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014670153&partnerID=8YFLogxK

U2 - 10.1515/phys-2016-0063

DO - 10.1515/phys-2016-0063

M3 - Article

AN - SCOPUS:85014670153

VL - 14

SP - 643

EP - 650

JO - Open Physics

JF - Open Physics

SN - 1895-1082

IS - 1

ER -