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**A new class of parallel algorithms for solving systems of linear equations.**
*(English)*
Zbl 0677.65021

Comparing the QR factorization with backsubstitution to Faddeev’s feed- forward method, the Faddeev’s array computes the solution roughly twice faster than QR factorization and substitution. It serves as a motivation for describing efficient noval feed-forward algorithms. It is shown how the backsubstitution can be rephrased in terms of an updating or downdating of a Cholesky factorization, or in terms of an LU factorization. It is explained how an LU, QR or \(LL^ t\) factorization of coefficient matrix is combined with the above rephrasing by which new feed-forward algorithms for solving systems of linear equations could be formed.

The systolic arrays for these methods are simple and with complexity in the order of a QR factorization. One of the methods (using only Givens rotations) is a numerically stable and robust method for the complete class of nonsingular systems. Simple extensions for these methods are also presented for computing expressions of the form \((B^ tA^{-t}C^ t+D^ t)\).

The systolic arrays for these methods are simple and with complexity in the order of a QR factorization. One of the methods (using only Givens rotations) is a numerically stable and robust method for the complete class of nonsingular systems. Simple extensions for these methods are also presented for computing expressions of the form \((B^ tA^{-t}C^ t+D^ t)\).

Reviewer: I.Arany

### MSC:

65F05 | Direct numerical methods for linear systems and matrix inversion |

65Y05 | Parallel numerical computation |

15A23 | Factorization of matrices |