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We present the first direct comparison of codes based on two differentnumerical methods for constructing rapidly rotating relativistic stars. A codebased on the Komatsu-Eriguchi-Hachisu (KEH) method (Komatsu et al. 1989),written by Stergioulas, is compared to the Butterworth-Ipser code (BI), asmodified by Friedman, Ipser and Parker. We compare models obtained by eachmethod and evaluate the accuracy and efficiency of the two codes. The agreementis surprisingly good. A relatively large discrepancy recently reported(Eriguchi et al. 1994) is found to arise from the use of two different versionsof the equation of state. We find, for a given equation of state, thatequilibrium models with maximum values of mass, baryon mass, and angularmomentum are (generically) all distinct and either all unstable to collapse orare all stable. Our implementation of the KEH method will be available as apublic domain program for interested users.Comment: 12 pages, AASTEX + 10 postscript figures and postscript version of  tex file, accepted for publication in the Astrophysical Journa

Comparing models of rapidly rotating relativistic stars constructed by two numerical methods