A note on down dating the cholesky factorization

23-Nov-2016 02:06

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(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.

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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.