jordan form of a floating point matrix

Hi there,

recently I stumbled across the jordan function that is now build-in in 2013a. And I wonder how it works on numerical matrices. Do you convert floating-point numbers to exact representation and eventually convert back to floating-point?

I was surprised to see that it computed the jordan form of an upper triangular matrix, with only ones on its diagonal and random entries above it, correctly. Since its jordan form is a single big jordan block of ones on the diagonal and superdiagonal. I guess if you would start doing floating point operations on it, you would blow the jordan form right off the start. can you say s.th. about the algorithms used, or give a reference?

Thank you in advance and regards

Paul