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

Djebar Baroudi

Research output: Book/ReportReport

Abstract

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.
Original languageEnglish
Place of PublicationEspoo
PublisherVTT Technical Research Centre of Finland
Number of pages34
ISBN (Print)951-38-4253-3
Publication statusPublished - 1993
MoE publication typeNot Eligible

Publication series

SeriesVTT Publications
Number135
ISSN1235-0621

Fingerprint

polynomials
intervals
confidence
computer programs
FORTRAN
curve fitting
preprocessing
approximation
finite element method
curvature
slopes
filters
oscillations

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

Baroudi, D. (1993). Piecewise least squares fitting technique using finite interval method with Hermite polynomials. Espoo: VTT Technical Research Centre of Finland. VTT Publications, No. 135
Baroudi, Djebar. / Piecewise least squares fitting technique using finite interval method with Hermite polynomials. Espoo : VTT Technical Research Centre of Finland, 1993. 34 p. (VTT Publications; No. 135).
@book{1b642bb8ce8e4d29a5a7741cacb021e4,
title = "Piecewise least squares fitting technique using finite interval method with Hermite polynomials",
abstract = "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.",
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",
author = "Djebar Baroudi",
note = "Project code: PALT9523",
year = "1993",
language = "English",
isbn = "951-38-4253-3",
series = "VTT Publications",
publisher = "VTT Technical Research Centre of Finland",
number = "135",
address = "Finland",

}

Baroudi, D 1993, 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.

Espoo : VTT Technical Research Centre of Finland, 1993. 34 p. (VTT Publications; No. 135).

Research output: Book/ReportReport

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 -

Baroudi D. Piecewise least squares fitting technique using finite interval method with Hermite polynomials. Espoo: VTT Technical Research Centre of Finland, 1993. 34 p. (VTT Publications; No. 135).