GCD search for non-integers

Does someone know how to solve this problem?

Find the approximation of greatest common divisor for a set of data (a vector of noninteger
numbers). In general, these will not have an exact common divisor. The solution
(also a floating point number) should be approximated with certain accuracy. E.g.:

    x = [3.3308 4.4449 7.7828 12.2273 14.4405 21.1161];
  epsilon = 0.01;
  d = find_gcd(x,epsilon)
  d =
  1.1111
  % verifying result
  x/d
  ans =
  2.9978 4.0005 7.0046 11.0046 12.9966 19.0047
  error = x/d – round(x/d)
  error =
  -0.0022 0.0005 0.0046 0.0046 -0.0034 0.0047

[Image Analyst]

Any number can divide those numbers. I think you need to add the requirement that after division, the result is within epsilon of an integer . Otherwise, yeah, you can divide any of those numbers by 500 bazillion and get another floating point number.

Answer 1

[Roger Stafford]

I see a way to do your problem provided it is assumed that each number in x must round to a non-zero integer. It would involve examining in order of decreasing magnitude the various values of a potential divisor at each point where one of the quantities in x divided by that divisor either enters or leaves an allowed epsilon interval about a non-zero integer. Since this looks like a homework problem I'll stop with that hint.