### Abstract

Original language | English |
---|---|

Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 34 |

ISBN (Print) | 951-38-4253-3 |

Publication status | Published - 1993 |

MoE publication type | Not Eligible |

### Publication series

Name | VTT Publications |
---|---|

Publisher | VTT |

No. | 135 |

ISSN (Print) | 1235-0621 |

ISSN (Electronic) | 1455-0849 |

### Fingerprint

### Keywords

- numerical analysis
- approxination
- finite element analysis
- computer programs
- utilization
- experimental data
- estimating
- least squares method
- curve fitting
- calculations
- functions (mathematics)
- confidence limits
- differential calculus
- temperature gradients
- mass flow
- combustion

### Cite this

*Piecewise least squares fitting technique using finite interval method with Hermite polynomials*. Espoo: VTT Technical Research Centre of Finland. VTT Publications, No. 135

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*Piecewise least squares fitting technique using finite interval method with Hermite polynomials*. VTT Publications, no. 135, VTT Technical Research Centre of Finland, Espoo.

**Piecewise least squares fitting technique using finite interval method with Hermite polynomials.** / Baroudi, Djebar.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Piecewise least squares fitting technique using finite interval method with Hermite polynomials

AU - Baroudi, Djebar

N1 - Project code: PALT9523

PY - 1993

Y1 - 1993

N2 - Experimental fire research often produces large amounts of data. Effective methods of preprocessing the data are needed to filter out irrelevant scatter and to make the data analysis easier. Curve fitting techniques are often needed to smooth out scattered experimental data to permit the application of analytical formulae which often involve derivatives of the data function. One of the critical features in fitting the data is to avoid discontinuous changes in curvature and slope, in cases where the associated oscillations in derivatives are physically meaningless. A working piecewise fitting technique based on the approximation technique of the finite element method is presented in association with the calculation of the confidence interval for the fitted function and its first and second derivatives. The approximation assumes the fitted function and its derivatives up to the second order to be continuous. The ideas presented below are then materialized into the creation of a performing software package programmed in standard FORTRAN 77. Given a sufficient set of data points (pairs) this software performs the fitting and calculates the confidence intervals of the fitted function, and its first and second derivatives.

AB - Experimental fire research often produces large amounts of data. Effective methods of preprocessing the data are needed to filter out irrelevant scatter and to make the data analysis easier. Curve fitting techniques are often needed to smooth out scattered experimental data to permit the application of analytical formulae which often involve derivatives of the data function. One of the critical features in fitting the data is to avoid discontinuous changes in curvature and slope, in cases where the associated oscillations in derivatives are physically meaningless. A working piecewise fitting technique based on the approximation technique of the finite element method is presented in association with the calculation of the confidence interval for the fitted function and its first and second derivatives. The approximation assumes the fitted function and its derivatives up to the second order to be continuous. The ideas presented below are then materialized into the creation of a performing software package programmed in standard FORTRAN 77. Given a sufficient set of data points (pairs) this software performs the fitting and calculates the confidence intervals of the fitted function, and its first and second derivatives.

KW - numerical analysis

KW - approxination

KW - finite element analysis

KW - computer programs

KW - utilization

KW - experimental data

KW - estimating

KW - least squares method

KW - curve fitting

KW - calculations

KW - functions (mathematics)

KW - confidence limits

KW - differential calculus

KW - temperature gradients

KW - mass flow

KW - combustion

M3 - Report

SN - 951-38-4253-3

T3 - VTT Publications

BT - Piecewise least squares fitting technique using finite interval method with Hermite polynomials

PB - VTT Technical Research Centre of Finland

CY - Espoo

ER -