So I have a function, say 'T' in Matlab that takes input vector 'x' and spits out vector 'y' in a linear fashion. I'm interested to know the largest real part of its Eigen-values and the corresponding Eigen-vector.
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If I could construct 'T' efficiently of course I would just use 'eigs' command with some options; but there is a step in the construction of 'T' that involves inverting a really big matrix– it becomes quite expensive and quickly becomes preventative in both RAM and CPU usages.
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So I want its eigenvalue/vector pairs without calculating the operator out explicitly and I realized that Python has a built-in for that — 'matvec', that takes a function and finds its Eigen-pairs. So far in Matlab I have yet to find the counterpart for it. (As a Matlab fan I'm not ready to convert to Python yet so help me out here lol).
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Let me know, thanks!
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ps: 'T' 's structure is some thing like T = A * B \ C *D ; A, B, C, D are sparse, and really big. Before exploring its sparseness and circulant properties I like to try this first. Thanks.
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