A note on down dating the cholesky factorization
(A, and C are also pos def) There is a formula for carrying out block Cholesky decomposition. So we have already calculated $A^$, and $C^$ (It is therefore straightforward to calculate the inverses $A^$, and $C^$ using forward substitution). The problem is indeed technical in its origin , but I'd hoped (perhaps naively) that the problem would also be of interest to other mathematicians.
Rewriting the Q in terms of these quantities we now have. The problem is related to the training a machine learning algorithm.
where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L.
However, the decomposition need not be unique when A is positive semidefinite.Our algorithm can utilize concurrency at different levels of the elimination tree by using multiple threads in both the CPU and the GPU.