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A couple of mistakes on sight: def RECTSPA(A,grid): """ description: what does this do ? """ m,n = A.shape I = np.eye(n) if m >= 2*n: a = A[n+1:m,:] # ◀◀◀ A[n:], python is 0-origin Q, R = np.linalg.qr(a) T, U = schur(a,output='real') R[0:n] # ◀◀◀...

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The eigenvalues given correspond to the flux jacobians in the Euler equations. Physically, they represent the speed at which waves of information can travel in a space-time domain. The goal is to compute the eigenvalues at each face based on the values in each neighboring cell so there is no 'left' or 'right' face in this equation, but instead a left and ...

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The Schur decomposition is a good solution for finding the eigen values and eigen vectors of a symmetric matrix. In MATLAB, use schur.m.

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It can be done. Back in the 1990s certain groups (think radar cross section computation) were working with 1,000,000 x 1,000,000 dense systems. Consistent with other replies, this was done iteratively and out of core.

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Let us proceed systematically: numerical precision of data (you said from medical imaging) number of operations required for standard methods (as from libraries) possible out-of-core computation (i.e. not the whole matrix at all times in memory). In all cases, I am afraid, you would have to be prepared to suffer. Incidentally, out-of-core methods are very ...

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Take a look at the literature that does similar things for facial recognition -- search for the term "eigenface", for example. The point to make in this context is that the information you are looking for does not actually require you to consider high-resolution images. You may have $10,000\times 10,000$ pixels, for which any non-trivial ...

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As noted above by Thijs Steel a randomized svd is a solution but the number 78800000 is out of our computers computation ability.So you can proceed to the rsvd algorithm by : import numpy as np n = 788 mu = 0 sigma = 1 A = np.random.normal(mu, sigma, (n,n)) Omega = np.random.normal(mu, sigma, (n,n)) def rsvd(A, Omega): Y = A @ Omega Q, _ = np....

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