Interpolation

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Interpolation

• Topic Spline Interpolation Method
• Major Electrical

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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.

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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.

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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)