The beheviours of both the error end the residual in the solution of a linear system are studied, by assuming representation and roundoff errors to be random variables. Two quantities which measure the mean value of the linear part of the error end the mean value of the linear part of the residual are introduced, giving stability and good behalviour criteria. These criteria are applied to various algorithms (Gaussian elimination with different types of pivoting, ortogonalization techniques). In addition the influence of row-scaling is studied.
Stability and good-behaviour of algorithms for solving linear systems
1986
Abstract
The beheviours of both the error end the residual in the solution of a linear system are studied, by assuming representation and roundoff errors to be random variables. Two quantities which measure the mean value of the linear part of the error end the mean value of the linear part of the residual are introduced, giving stability and good behalviour criteria. These criteria are applied to various algorithms (Gaussian elimination with different types of pivoting, ortogonalization techniques). In addition the influence of row-scaling is studied.File in questo prodotto:
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Descrizione: Stability and good-behaviour of algorithms for solving linear systems
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