Sparse Matrix Algorithms |
The conjugate gradient algorithm can be interpreted as the following
optimization problem: minimize defined by
At each iteration is minimized along an
-conjugate
direction, constructing orthogonal residuals:
Minimum residual algorithms work by minimizing the Euclidean norm over
. At each iteration,
is the vector in
that gives the smallest residual.
The biconjugate gradient algorithm belongs to a more general class
of Petrov-Galerkin methods, where orthogonality is enforced in a
different -dimensional subspace (
remains in
):
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