The following files give complete timings for eigensolve and mpsolve on most of the polynomials on the MPSolve web site.  In all cases, both programs computed all roots to at most the relative error specified by the number of decimal digits.  (The command "unisolve -Ga -on  file" was used for mpsolve and "eigensolve -on -i200 file" for eigensolve.)  A polynomial may have been  skipped because the running time was too large, or because the format of the file was inappropriate.

•  Linux g++ on 800 Mhz Pentium 3;  15 digits
•   SGI CC on 250 Mhz SGI R10000; 15 digits
•   SGI CC on 250 Mhz SGI R10000; 50 digits

• For dense, ill-conditioned polynomials (Wilkinson, Chebyshev, Laguerre, Legendre, Sendra etc.), both programs are relatively slow, but eigensolve is much faster than mpsolve.
• For well-conditioned polynomials (e.g. `easy', 'sparsennn'), mpsolve is faster than eigensolve.  In some cases, for example polynomials of degree d several hundred or more,  mpsolve reports roots significantly faster than a single floating-point eigenvalue computation on a dxd matrix.
• Mpsolve takes advantage of sparsity, and has special hooks for polynomials that can be evaluated efficiently by straight-line programs.  In these cases mpsolve has an advantage.