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Richardson Extrapolation

09 Jun 2009 (Updated 09 Jun 2009)

Code covered by the BSD License

A generalized Richardson extrapolation routine with many bells and whistles.

File Information
Description	A generalized Richardson extrapolation routine that can perform multiple extrapolation steps, can accommodate arbitrary leading error terms, can handle any uniform refinement scheme (e.g. h/2, h/3, h/5, etc), and can report a full extrapolation table including comparing against a known good solution. Able to handle vector inputs. Compatible both with MATLAB and Octave. Includes Octave-style unit tests. A contrived usage example: Suppose your sequence of approximations was [1, 2, 3, 4] where each successive value refined the grid by a factor of 3. Suppose the three leading error terms in the approximation were O(h^2), O(h^4), and O(h^5) and that you knew the exact value was 4.14. Then you'd invoke octave:78> [result, normtable] = richardson([1,2,3,4],[2,4,5], 3, 4.14) result = 4.14163223140496 normtable = 3.13999999999999968 NaN NaN NaN 2.13999999999999968 2.01499999999999968 NaN NaN 1.13999999999999968 1.01499999999999968 1.00249999999999950 NaN 0.13999999999999968 0.01499999999999968 0.00249999999999950 0.00163223140495905 which shows you the exact result and a full extrapolation table showing the l2 error at each substep. For more normal examples with h/2 refinement, more standard leading error terms (e.g. starting at h^2 and increasing by h or h^2), and unknown exact solutions the function has much default magic to simplify input parameters.
MATLAB release	MATLAB 7.6 (R2008a)
Zip File Content
Other Files	license.txt, richardson.m

Tags for This File
Everyone's Tags	approximation, estimation, extrapolation, polynomial, richardson, taylor
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Updates
09 Jun 2009	Fixed a typo or two in the text. No code change.

Tag Activity for this File
Tag	Applied By	Date/Time
taylor	Rhys	09 Jun 2009 16:21:42
approximation	Rhys	09 Jun 2009 16:22:04
extrapolation	Rhys	09 Jun 2009 16:22:04
richardson	Rhys	09 Jun 2009 16:22:04
estimation	Rhys	09 Jun 2009 16:22:04
polynomial	Rhys	09 Jun 2009 16:22:04

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