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Variationally derived algorithms in the ABS class for linear systems
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Calcolo, Vol. 24, No. 3. (1 December 1987), pp. 241-246.
Abstract
Abstract Algorithms in the ABS class of direct methods for linear systems are considered where the correction to the projection matrix minimizes a weighted Frobenius norm. These algorithms define implicit factorizations of the coefficient matrix which do not require pivoting. The implicit Gram-Schmidt algorithm is obtained when using the unweighted norm.
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