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Apr 29, 2012 at 14:08 comment added Felix Goldberg Well, actually it's $\alpha$ that's varying and $s$ is fixed. Thanks for the reference, I'll be sure to read.
Apr 26, 2012 at 4:52 comment added Brian Borchers Let me also mention that if $\alpha$ is fixed and you want to vary $s$, then you might find that a better way to go is to compute the eigenvalue decomposition of $Q-\alpha J$, and then adjust for $sI$ by adding $s$ to the eigenvalues.
Apr 26, 2012 at 1:02 comment added Brian Borchers A classic reference (and the paper is available online as a free .pdf) is: P. Gill, G. Golub, W. Murray, and M. Saunders. Methods for modifying matrix factorizations. Mathematics of Computation, 126(28):505-535, 1974. stanford.edu/group/SOL/papers/ggms74.pdf
Apr 25, 2012 at 8:35 vote accept Felix Goldberg
Apr 25, 2012 at 7:53 comment added Felix Goldberg Thanks! Can you give me a particular reference? My focus is on theory, not computation.
Apr 25, 2012 at 1:23 history answered Brian Borchers CC BY-SA 3.0