Arithmetic and Space Complexity.

It is quite a costly procedure to compute a GUPTRI form and associated error bounds. In the worst case (e.g., a generic $(n+1) \times n$ pencil), GUPTRI requires $O(n^4)$ floating point operations. The storage requirements of each routine are discussed in [122] (sections 3 and 7). The real bottleneck in the present software is the workspace required by the routine BOUND and the computations performed therein. There is a routine (BNDWSP) that computes the exact amount of workspace needed in the routine BOUND.