How effective is the nuclear norm heuristic in solving data approximation problems?

The question in the title is answered empirically by solving instances of three classical problems: fitting a straight line to data, fitting a real exponent to data, and system identification in the errors-in-variables setting. The results show that the nuclear norm heuristic performs worse than alternative problem dependant methods—ordinary and total least squares, Kung's method, and subspace identification. In the line fitting and exponential fitting problems, the globally optimal solution is known analytically, so that the suboptimality of the heuristic methods is quantified.