Simplest Interpolating Polynomial

  • Thread starter Thread starter chronicals
  • Start date Start date
  • Tags Tags
    Polynomial
Click For Summary
SUMMARY

The discussion focuses on determining the simplest interpolating polynomial for constant-pressure specific heat (Cp) data across various temperatures (T). The provided temperature data points are 1000 K to 1500 K, with corresponding Cp values ranging from 1.1573 kJ/kg.K to 1.410 kJ/kg.K. The user expresses confusion regarding the appropriate method to use, specifically distinguishing between polynomial interpolation methods such as Newton's and Lagrange's, while excluding least squares and regression techniques. It is concluded that both Newton's and Lagrange's methods will yield the same fifth-degree polynomial for the given data.

PREREQUISITES
  • Understanding of polynomial interpolation techniques, specifically Newton's and Lagrange's methods.
  • Familiarity with constant-pressure specific heat (Cp) concepts in thermodynamics.
  • Basic knowledge of data analysis and numerical methods.
  • Ability to work with temperature data and corresponding physical properties.
NEXT STEPS
  • Study the implementation of Newton's interpolating polynomial in numerical analysis.
  • Explore Lagrange's interpolation formula and its applications in data fitting.
  • Learn about error analysis in polynomial interpolation to ensure predictions are within acceptable limits.
  • Review case studies on the application of polynomial interpolation in thermodynamic properties.
USEFUL FOR

Students and professionals in engineering, particularly those studying thermodynamics and numerical methods, as well as anyone involved in data interpolation and analysis.

chronicals
Messages
35
Reaction score
0

Homework Statement


Consider the data in the following table for constant-pressure specific heat, C
p (kJ/kg.K) at various temperatures T (K). Determine the simplest interpolating polynomial that is likely to predict Cp within 1% error over the specified range of temperature.

T : 1000 1100 1200 1300 1400 1500
Cp 1.410 1.1573 1.1722 1.1858 1.1982 1.2095




Homework Equations





The Attempt at a Solution


I am very confused, i am studying ''general least squares,polynomial regression, linear regression, Newton's interpolating polynomials, lagrange interpolating polynomials'' now. I have a question but i don't know which method i should use, can you help me quickly? Thanks. This is my question:
 
Physics news on Phys.org
Since the problem says "interpolating polynomials", that let's out any least squares or regression- and, here, both Newton's and Lagrange's methods should give the same fifth degree polynomial.
 

Similar threads

Undergrad Proof for interpolating polynomial and error approximation
  • · Replies 6 ·
Replies
6
Views
2K
Lagrange and cubic spline interpolate
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Difference calculating enthalpy change by using thermodynamic table A-17 vs. A-2 with integration
  • · Replies 1 ·
Replies
1
Views
906
Substitute PID Controls with a Polynomial Equation/Table?
  • · Replies 3 ·
Replies
3
Views
2K
How Do You Solve a 7th Degree Polynomial Interpolation by Hand for Given Points?
  • · Replies 3 ·
Replies
3
Views
2K
Lagrange interpolation formula
  • · Replies 1 ·
Replies
1
Views
3K
Lagrange Interpolation and Matrices
  • · Replies 1 ·
Replies
1
Views
2K
Is there a way to transform a polynomial into a vector?
  • · Replies 9 ·
Replies
9
Views
2K
Interpolation using divided differences
  • · Replies 3 ·
Replies
3
Views
2K
Is Spline Interpolation an FIR Filter
  • · Replies 2 ·
Replies
2
Views
2K