splitting

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The splitting displayed below was calculated on the base of (2) for n = 3 .
matrix norm bounds, two-norm, norm bounds for sparse matrices, splitting lemma, support theory, support preconditioning
Support theory employs two devices to bound the support of a preconditioner: one is the splitting lemma [1, 9], and the other is the symmetric product support lemma [5].
In early support-theory papers [1, 9], three main tools were used: the support lemma, the splitting lemma and the congestion-dilation lemma.
They also show that the bounds that were previously derived by the splitting and congestion-dilation lemmas can be directly obtained by applying their new lemma together with the norm bound [[parallel]W[parallel].
The following splittings are stable, the condition numbers depend on the coefficients [c.
Among the splittings presented above, we are interested most in the splittings (5.
For refining the other splittings they do depend on [c.
Applying the additive subspace correction method on one of the splittings (5.
Since [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then both splittings are convergent.
1 we obtain the convergence of Algorithm 3, and therefore of Algorithm 2, applied to Hermitian positive definite matrices, when all outer splittings are the same, and both inner and outer splittings are P-regular.
When A is Hermitian and positive definite, algorithms 2 and 3 may not converge even if the splittings are P-regular.

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