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First, if $A$ is s.p.d, and $L = [l_]$, then necessarily, both $i$ and $j$ will range to $n$, as $L$ is an $n \times n$ lower triangular matrix.For the algorithm itself, though, we do limit the range of $i$ and $j$ since, by definition, we need only compute the lower triangular portion of the matrix.I recently asked this question asking for an efficient way to compute the Mahalanobis distance (without calculating the inverse).The accepted solution was to use the Cholesky factorization and forward selection.However, when in my experiments in MATLAB I have seen that while Cholesky factorization is indeed faster than computing the inverse, the solution involving the inverse is more accurate.
(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.A linear systolic array of computation cells, each cell having several vector rotation stages.These stages are programmable to provide efficient implementation of a variety of matrix algorithms.Can you please give us an actual numerical example?Please also see the implementation note I did in your previous thread.

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