Difference between revisions of "Interpolation"

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== Linear Interpolation ==
 
== Linear Interpolation ==
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=== Example ===
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==== Implementation in Matlab ====
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==== Implementation in Excel ====
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== Polynomial Interpolation ==
 
== Polynomial Interpolation ==
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=== Example ===
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==== Implementation in Matlab ====
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== Cubic Spline Interpolation ==
 
== Cubic Spline Interpolation ==
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=== Example ===
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==== Implementation in Matlab ====
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Revision as of 08:59, 15 July 2008

Linear Interpolation

Example

Implementation in Matlab

Implementation in Excel

Polynomial Interpolation

Example

Implementation in Matlab

Cubic Spline Interpolation

Example

Implementation in Matlab

Lagrange Polynomial Interpolation

Given n_p points (x_k,y_k), the n^\mathrm{th} order Lagrange polynomial that interpolates these function values, f(x) are expressed as

f(x)=\sum_{k=0}^{n} y_{k} L_{k}(x),

where L_{k}(x) is the Lagrange polynomial given by

L_{k}(x)=\prod_{\stackrel{i=0}{i\ne k}}^{n}\frac{x-x_{i}}{x_{k}-x_{i}},

and n_p = n+1. In other words, for an n^\mathrm{th} order interpolation, we require n_p=n+1 points.

The \prod operator represents the continued product, and is analogous to the \sum operator for summations. For example, \prod_{i=1}^{3} (x+i) = (x+1)(x+2)(x+3).

Example

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