# A note on down dating the cholesky factorization In this note we briefly describe our Cholesky modification algorithm for streaming multiprocessor architectures.Our implementation is available in C with Matlab binding, using CUDA to utilise the graphics processing unit (GPU).

In this note we briefly describe our Cholesky modification algorithm for streaming multiprocessor architectures.Our implementation is available in C with Matlab binding, using CUDA to utilise the graphics processing unit (GPU).

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Limited speed ups are possible due to the bandwidth bound nature of the problem.

Furthermore, a complex dependency pattern must be obeyed, requiring multiple kernels to be launched.

Here is my progress: If $M = \begin a& 0 \\ u&C \end$, then since we have $\begin a& 0 \\ u&C \end \begin a& u^T \\ 0&C^T \end = \begin k& v^ \\ v&A \end$, we get $k=a^$, $v=au$, $uu^ CC^ = LL^$ as $A=LL^$.

Hence $a = \sqrt$, $u = v/\sqrt$, therefore, $a$ and $u$ can be represented in terms of $k$ and $v$.

However, I'm stuck on representing $C$ in terms of $k$, $v$ and $L$.

Although I have $CC^=LL^-uu^$, I don't know how to start from here. This problem seems to be called rank-one downdating of the Cholesky decomposition.

By showing that the new algorithm saves forty percent purely redundant operations of the original, better stability properties are expected.

In addition, various other downdating algorithms are rederived and analyzed under a uniform framework.