In mathematics, minimum polynomial extrapolation is a sequence transformation used for convergence acceleration of vector sequences, due to Cabay and Jackson.
[1] While Aitken's method is the most famous, it often fails for vector sequences.
An effective method for vector sequences is the minimum polynomial extrapolation.
It is usually phrased in terms of the fixed point iteration: Given iterates
,
, one constructs the
matrix
whose columns are the
differences.
Then, one computes the vector
denotes the Moore–Penrose pseudoinverse of
The number 1 is then appended to the end of
, and the extrapolated limit is where
is the matrix whose columns are the
iterates starting at 2.
The following 4 line MATLAB code segment implements the MPE algorithm:
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