Newton

1
Newtons Divided Difference Polynomial Method of
Interpolation

• Electrical Engineering Majors
• Authors Autar Kaw, Jai Paul
• http//numericalmethods.eng.usf.edu
• Transforming Numerical Methods Education for STEM
  Undergraduates

2
Newtons Divided Difference Method of
Interpolation http//numericalmethods.eng.us
f.edu
3
What is Interpolation ?

Given (x0,y0), (x1,y1), (xn,yn), find the
value of y at a value of x that is not given.
4
Interpolants

• Polynomials are the most common choice of
  interpolants because they are easy to
• Evaluate
• Differentiate, and
• Integrate.

5
Newtons Divided Difference Method

• Linear interpolation Given
  pass a linear interpolant through the data
• where

6
Example

• Thermistors are based on materials change in
  resistance with temperature. A manufacturer of
  thermistors makes the following observations on a
  thermistor. Determine the temperature
  corresponding to 754.8 ohms using the Newton
  Divided Difference method for linear
  interpolation.

R (O) T(C)
1101.0 911.3 636.0 451.1 25.113 30.131 40.120 50.128
7
Linear Interpolation
8
Linear Interpolation (contd)
9
Quadratic Interpolation
10
Example

• Thermistors are based on materials change in
  resistance with temperature. A manufacturer of
  thermistors makes the following observations on a
  thermistor. Determine the temperature
  corresponding to 754.8 ohms using the Newton
  Divided Difference method for quadratic
  interpolation.

R (O) T(C)
1101.0 911.3 636.0 451.1 25.113 30.131 40.120 50.128
11
Quadratic Interpolation (contd)


12
Quadratic Interpolation (contd)
13
Quadratic Interpolation (contd)
14
General Form
where


Rewriting
15
General Form
16
General form
17
Example

• Thermistors are based on materials change in
  resistance with temperature. A manufacturer of
  thermistors makes the following observations on a
  thermistor. Determine the temperature
  corresponding to 754.8 ohms using the Newton
  Divided Difference method for cubic
  interpolation.

R (O) T(C)
1101.0 911.3 636.0 451.1 25.113 30.131 40.120 50.128
18
Example

19
Example
20
Example
21
Comparison Table
22
Actual Calibration
R (O) T (C) x(ln R) y(1/T)
1101.0 911.3 636.0 451.1 25.113 30.131 40.120 50.128 7.0040 6.8149 6.4552 6.1117 0.039820 0.033188 0.024925 0.019949
23
Actual Calibration
24
Actual Calibration
25
Actual Calibration
26
Actual Calibration
27
Additional Resources

• For all resources on this topic such as digital
  audiovisual lectures, primers, textbook chapters,
  multiple-choice tests, worksheets in MATLAB,
  MATHEMATICA, MathCad and MAPLE, blogs, related
  physical problems, please visit
• http//numericalmethods.eng.usf.edu/topics/newton_
  divided_difference_method.html

28

• THE END
• http//numericalmethods.eng.usf.edu