1

I'm not sure if this is possible but I'm looking for a way to reverse engineer a given matrix (preferably subjected to a parameter).

H_{ij} = \frac{1}{i+j-1}.

For example, given a Hilbert Matrix, I want to get the generating function

Thank you for all the help in advance.

mkierc
  • 1,193
  • 2
  • 15
  • 28
kirikoumath
  • 723
  • 9
  • 20
  • 3
    This would mean to find an interpolating function so that a_ij=f(i,j). You can do a least square fit for a rational function that has some degree bound, this should also solve the test case of the Hilbert matrix. The utility of this approach is doubtful, most useful matrices do not have such a "smooth" functional structure. Similar topics are techniques for model reduction and compressive sensing. – Lutz Lehmann Apr 27 '14 at 19:37
  • @LutzL: that “comment” of yours sounds very much like an answer to me. – MvG Apr 28 '14 at 06:52

0 Answers0