minimum_polynomial module¶

The minimum polynomial method.

class gemseo.algos.sequence_transformer.acceleration.minimum_polynomial.MinimumPolynomial(window_size=5)[source]¶

Bases: SequenceTransformer

The minimum polynomial extrapolation method.

The method is introduced in: Cabay, S.; Jackson, L.W, “A polynomial extrapolation method for finding limits and antilimits of vector sequences”, SIAM Journal on Numerical Analysis, (1976).

Parameters:

window_size (int) –

The maximum number of iterates to be kept.

By default it is set to 5.

clear()¶

Clear the iterates.

Return type:: None

compute_transformed_iterate(iterate, residual)¶

Compute the next transformed iterate.

Parameters:

iterate (NDArray) – The iterate \(G(x_n)\).
residual (NDArray) – The associated residual \(G(x_n) - x_n\).

Returns:

The next transformed iterate \(x_{n+1}\).

Return type:

NDArray