On 05/02/2012 01:38 AM, Russ P. wrote:
On May 1, 4:05 pm, Paul Rubin<no.em...@nospam.invalid> wrote:
someone<newsbo...@gmail.com> writes:
Actually I know some... I just didn't think so much about, before
writing the question this as I should, I know theres also something
like singular value decomposition that I think can help solve
otherwise illposed problems,
You will probably get better advice if you are able to describe what
problem (ill-posed or otherwise) you are actually trying to solve. SVD
just separates out the orthogonal and scaling parts of the
transformation induced by a matrix. Whether that is of any use to you
is unclear since you don't say what you're trying to do.
I agree with the first sentence, but I take slight issue with the word
"just" in the second. The "orthogonal" part of the transformation is
non-distorting, but the "scaling" part essentially distorts the space.
At least that's how I think about it. The larger the ratio between the
largest and smallest singular value, the more distortion there is. SVD
may or may not be the best choice for the final algorithm, but it is
useful for visualizing the transformation you are applying. It can
provide clues about the quality of the selection of independent
variables, state variables, or inputs.
Me would like to hear more! :-)
It would really appreciate if anyone could maybe post a simple SVD
example and tell what the vectors from the SVD represents geometrically
/ visually, because I don't understand it good enough and I'm sure it's
very important, when it comes to solving matrix systems...
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