On systolic arrays for updating the Cholesky factorization
The authors are concerned with finding the Cholesky factors of a matrix \(B=A+\sum^{k}_{1}\alpha_ iz_ iz^ T_ i\) when the factors of A, the constants \(\alpha_ i\) and the vectors \(z_ i\) are known. They implement algorithms studied by \textit{P. Gill}, \textit{G. Golub}, \textit{W. Murray} and \textit{M. Saunders} [(*) Math. Comput. 28, 505-535 (1974; Zbl 0289.65021)] on systolic arrays involving plane rotations [e.g., the first author, BIT 26, 303-316 (1986; reviewed above)]. When \(\alpha_ i>0\) for \(i=1,...,k\), an algorithm from (*) is implemented in a single-pass array. When some \(\alpha_ i\leq 0\), the authors first generalize an algorithm from (*) and then show it can be implemented in a two-pass array.
scientific article; zbMATH DE number 4001299