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# Spline Interpolation

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Basic spline interpolation

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### Spline Interpolation

1. 1. Interpolation Topic: Spline Interpolation Method Major: General
2. 2. What is Interpolation ? Given (x 0 ,y 0 ), (x 1 ,y 1 ), …… (x n ,y n ), find the value of ‘y’ at a value of ‘x’ that is not given.
3. 3. Interpolants <ul><li>Polynomials are the most common choice of interpolants because they are easy to: </li></ul><ul><ul><li>Evaluate </li></ul></ul><ul><ul><li>Differentiate, and </li></ul></ul><ul><ul><li>Integrate . </li></ul></ul>
4. 4. Why Splines ?
5. 5. Why Splines ? Figure : Higher order polynomial interpolation is a bad idea
6. 6. Linear Interpolation
7. 7. Linear Interpolation (contd)
8. 8. Example <ul><li>The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using linear splines. </li></ul>Table : Velocity as a function of time Figure : Velocity vs. time data for the rocket example 901.67 30 602.97 22.5 517.35 20 362.78 15 227.04 10 0 0 m/s s v(t) t
9. 9. Linear Interpolation