BICGSTABBi-Conjugate Gradient-Stable Algorithm
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If the latter are chosen as in BICGSTAB (and they usually are), and if [[?
So there remains the question whether and how BICGSTAB and IDR(1) differ.
Comparison with the recursions and orthogonality properties of BICGSTAB.
3h) upon which BICGSTAB builds too, are mirrored by the following recursions for [[rho].
2j+1] in terms of quantities from BICGSTAB and the IDR coefficient [[gamma].
2j-1], is indeed the same in IDR(1) and BICGSTAB, since [v.
This case is easy, because in exact arithmetic the even-indexed IDR(1) iterates and residuals are exactly the BICGSTAB iterates and residuals.
While IDR(1) and BICGSTAB produce in exact arithmetic essentially the same results based on a common mathematical background, they are clearly different algorithms obtained by different approaches.
BICGSTAB ~ IDR(1) is matched by the relation ML(s)BICG [?
A similar improvement of the condition of the basis can be expected when we compare BICGSTAB to ML(s)BICGSTAB or IDR(s), and it seems to be relevant also in preconditioned problems that are not extremely ill-conditioned.
j] = j(s +1), this ratio is 1 + 1/s, while for CGS and BICGSTAB it is 2.
IDR(s) also inherits from BICGSTAB the disadvantage that for a problem with real-valued data, the parameters [[omega].