A Cholesky Up- and Downdating Algorithm for Systolic and SIMD Architectures

This paper presents an algorithm for maintaining Cholesky factors of symmetric positive definite matrices under arbitrary rank-one changes. The algorithm synthesizes Carlson’s up-dating algorithm, and the downdating algorithm recently suggested by Pan to arrive at an algorithm which is both simple and allows for the pipelining of up- and downdates (in any order). On an array of $O(n^2 )$ processors, the algorithm allows an $n \times n$ matrix to be updated at a cost per update that is independent of n. Implementation results on the 1024-processor AMT DAP-510 emphasize the simplicity and practicality of the proposed scheme.