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I'm facing a problem in performing incomplete Cholesky decomposition of sparse matrices. I use the algorithm which avoids talking square roots, given in here: http://en.wikipedia.org/wiki/Cholesky_decomposition and apply it to sparse matrices by just skipping the zeros ( no filling). My matrices are certainly symmetric and positive definite but the algorithm sometimes give negative diagonal elements. I have two questions regarding this:

1. Is this the consequence of ignoring zero elements in the sparse matrices or is due to error accumulation?

2. In order to go around the problem, I multiply the diagonal values by a number larger than 1.0, before decomposition. For small matrices, 1.05 may be enough but as the matrix sizes grows, the factor is not large enough. However with factor 1.2, the algorithm has never given negative diagonal values even for matrices of 1000,000 by 1000,000. Does anyone have any explanation as why the number helps and what is the smallest number which assure all positive diagonal elements?

Your help would be appreciated.

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# Negative diagonal elements in Incomplete Cholesky Decompostion

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