### 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 language | English |
---|---|

Pages (from-to) | 643-650 |

Number of pages | 8 |

Journal | Open Physics |

Volume | 14 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2016 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Open Physics*,

*14*(1), 643-650. https://doi.org/10.1515/phys-2016-0063

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

Research output: Contribution to journal › Article

*Open Physics*, vol. 14, no. 1, pp. 643-650. https://doi.org/10.1515/phys-2016-0063

}

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 -