Solution of linear least squares via the ABS algorithm
The authors consider the application of ABS methods to the solution of overdetermined linear systems \(Ax=b\) arising in least squares problems. The general class of ABS algorithms is described in the paper by \textit{J. Abaffy}, \textit{C. G. Broyden} and the first author [Numer. Math. 45, 361- 387 (1985; Zbl 0535.65009)]. This paper gives the specific form required for the least squares implementation, again using rank-one updates for the reflection matrix \(H\). Six implementations are briefly described and the second part describes the results of extensive numerical experiments with these implementations. The authors conclude that an explicit Gram-Schmidt factorization incorporated into a modified Huang algorithm generally gives better results than the NAG QR code, though the latter has smaller overheads.
scientific article; zbMATH DE number 221260