Rational polynomials
- Univ. of Auckland (New Zealand). Dept of Engineering Science
Numerical analysis is an important part of Engineering. Frequently relationships are not adequately understood, or too complicated to be represented by theoretical formulae. Instead, empirical approximations based on observed relationships can be used for simple fast and accurate evaluations. Historically, storage of data has been a large constraint on approximately methods. So the challenge is to find a sufficiently accurate representation of data which is valid over as large a range as possible while requiring the storage of only a few numerical values. Polynomials, popular as approximation functions because of their simplicity, can be used to represent simple data. Equation 1.1 shows a simple 3rd order polynomial approximation. However, just increasing the order and number of terms included in a polynomial approximation does not improve the overall result. Although the function may fit exactly to observed data, between these points it is likely that the approximation is increasingly less smooth and probably inadequate. An alternative to adding further terms to the approximation is to make the approximation rational. Equation 1.2 shows a rational polynomial, 3rd order in the numerator and denominator. A rational polynomial approximation allows poles and this can greatly enhance an approximation. In Sections 2 and 3 two different methods for fitting rational polynomials to a given data set are detailed. In Section 4, consideration is given to different rational polynomials used on adjacent regions. Section 5 shows the performance of the rational polynomial algorithms. Conclusions are presented in Section 6.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Auckland Univ. (New Zealand). Dept. of Engineering Science
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 270796
- Report Number(s):
- LA-SUB-96-84; ON: DE96013683; TRN: AHC29617%%128
- Resource Relation:
- Other Information: PBD: Feb 1996
- Country of Publication:
- United States
- Language:
- English
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