Variations on the Gram–Schmidt and the Huang algorithms for linear systems: A numerical study. (English) Zbl 0783.65029
Results of extensive numerical experiments with algorithms for linear systems based on \(LQ\), \(QR\), and Huang type methods are presented. It is shown that the best modified Huang algorithms are essentially as good as the doubly iterated Gram-Schmidt algorithm, applied on the rows of the coefficient matrix and coupled with the \(ABS\) update formula. They are generally more accurate than the stabilized Gram-Schmidt algorithm and the algorithms based on the \(QR\) factorization.
Reviewer: R.P.Tewarson (Stony Brook)
MSC:
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
ill-conditioned equations; \(QR\) method; \(LQ\) method; Huang methods; numerical experiments; algorithms; Huang algorithms; Gram-Schmidt algorithm; \(ABS\) update formulaReferences:
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