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How a direct method can be compared with an iterative method? I have an iterative method to compute Moore- penrose generalized inverse. There are some direct methods available to compute Moore-Penrose generalized inverse such as singular value decomposition and QR factorization etc. I want to compare my iterative methods with these direct methods. In what context shoul i compare?

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Maybe not answering you concern but I would like to let you know that now we have a dedicated SE site for numerical methods: Computational Science –  Shuhao Cao May 8 '12 at 4:25
But internally, SVD is an iterative method! Those singular values aren't computed exactly, you know... –  J. M. May 8 '12 at 4:28
I am not getting your point sir. –  srijan May 8 '12 at 4:31
@srijan A typical way to compare is to take a known solution say $x$ and compute $b = Ax$. Assuming your matrix vector product is error free, compute the solution using your iterative method ($x_i$) and using your "direct" method ($x_e$). Now look at the relative error in the solution obtained by these two methods and also compare the time taken by these two algorithms. –  user17762 May 8 '12 at 4:42
It is not clear to me what the distinction is, or why it matters. For example, is Conjugate Gradient an iterative or direct method? Perhaps an iterative method is one that produces an 'improved solution' at each iteration (down to a noise floor, of course)? –  copper.hat May 8 '12 at 5:10

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