Crout Algorithm with Accumulated Inner Product
AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OH
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A posteriori forward error analysis is applied to the Crout algorithm with inner product accumulation in solving system of linear algebraic equations of the type Ax b. By attributing the generated round-off errors properly to the matrices A and b, it is shown, under certain reasonable assumptions, that the computed x satisfies a new perturbed system such that A delta Ax b delta b and the upper bounds for delta A and delta b in infinite norm are shown to be proportional to n, the system order. This is an improvement over the results where the inner products are not accumulated.
- Theoretical Mathematics