Spline Interpolation Method

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Spline Interpolation Method

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

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Spline Method of Interpolation
http//numericalmethods.eng.usf.edu
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What is Interpolation ?

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

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

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Why Splines ?
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Why Splines ?
Figure Higher order polynomial interpolation is
a bad idea
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Linear Interpolation
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Linear Interpolation (contd)
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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 linear spline
  interpolation.

R (O) T(C)
1101.0 911.3 636.0 451.1 25.113 30.131 40.120 50.128
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Linear Interpolation




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Quadratic Interpolation
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Quadratic Interpolation (contd)
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Quadratic Splines (contd)
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Quadratic Splines (contd)
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Quadratic Splines (contd)
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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 quadratic
  spline interpolation.

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




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Solution (contd)
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Solution (contd)
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Solution (contd)
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Solution (contd)
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Solution (contd)
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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/spline
  _method.html

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