gemseo / algos / sequence_transformer / acceleration

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aitken module

The Aitken’s acceleration method.

class gemseo.algos.sequence_transformer.acceleration.aitken.Aitken[source]

Bases: SequenceTransformer

The vector Δ²-Aitken acceleration method.

The method is introduced in: Isabelle Ramiere, Thomas Helfer, “Iterative residual- based vector methods to accelerate fixed point iterations”, Computers and Mathematics with Applications, (2015) eq. (45).

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