>> proj1demo

PROJ1DEMO
  This function shows how to work with Kronecker products and SVD's.

  Suppose K = kronecker_product ( A, B )
  Suppose we want to solve K*f=g
  using the singular value decomposition of K.

  In this example, we choose random values for
  f, A and B, then compute K and g.

  Instead of solving K*f=g by taking the SVD of K
  we compute the SVD's of A and B, which implicitly
  define the SVD of K.  Then we can determine the solution f
  and we never actually formed the SVD of K, and we really
  never had to form K either.

  The matrices A and B will be 3x3

  The matrix K will have order 9x9

  There are two ways to form the right hand side g.
  To show they are the same, here is the norm of their difference:

  norm(G - g) = 8.082546e-16

  Here is the error between the exact solution F
  and the solution we computed:

  norm(F - Fc) = 1.808874e-14

  Now let's show that we really can compute the SVD of K.
  Does the product U * S * V' = K?

  Norm ( K - U*S*V' ) = 3.797148e-15

  Is our U matrix orthogonal?
  norm ( U*U'-I ) = 1.256964e-15

  Is our V matrix orthogonal?
  norm ( U*V'-I ) = 9.033210e-16

PROJ1DEMO:
  Normal end of execution.
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