gemseo / algos / sequence_transformer / acceleration

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alternate_2_delta module

The alternate 2-δ acceleration method.

class gemseo.algos.sequence_transformer.acceleration.alternate_2_delta.Alternate2Delta

Bases: SequenceTransformer

The alternate 2-δ 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. (50).

The least squares problem that must be solved to perform the transformation may be degenerated when the vectors \(x_{n+1} - x_n\) and \(x_n - x_{n-1}\) are collinear.

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