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An improvement of the radial-velocity measurement accuracy is crucial for the detection of tiny stellar oscil- lations and exoplanets. Through the analysis of week-long extensive observations of solar-type stars (Procyon in 2000, 2002, and 2006/2007 and Cet in 2002 and 2006/2007), we have carefully examined, revised, and finely tuned the widely used multiple Gaussian IP fitting method for the spectrograph, HIDES. By determining a necessary and sufficient number of free parameters in the model as well as introducing an iterative process in the radial-velocity analysis, we can reach a precision of below 3 m s 1 , which is much smaller than the precision of 6 m s 1 officially announced so far for HIDES. We also make our technique refined for the 2002 McDonald Procyon data. Even with our revised method, slow radial velocity variations with an amplitude of about 10 m s 1 are left in the Procyon data. We emphasize that it is neither due to particular observing instruments nor radial-velocity analysis, and thus could be due to stellar origin. The analysis presented here makes the foundations of our next scientific analysis of the radial-velocity variations of Procyon, which will be presented in our forthcoming papers.

Hubble Space Telescope observations of the nearby (3.22 pc), K2 V star epsilon Eridani have been combined with ground-based astrometric and radial velocity data to determine the mass of its known companion. We model the astrometric and radial velocity measurements simultaneously to obtain the parallax, proper motion, perturbation period, perturbation inclination, and perturbation size. Because of the long period of the companion, \eps b, we extend our astrometric coverage to a total of 14.94 years (including the three year span of the \HST data) by including lower-precision ground-based astrometry from the Allegheny Multichannel Astrometric Photometer. Radial velocities now span 1980.8 -- 2006.3. We obtain a perturbation period, P = 6.85 +/- 0.03 yr, semi-major axis, alpha =1.88 +/- 0.20 mas, and inclination i = 30.1 +/- 3.8 degrees. This inclination is consistent with a previously measured dust disk inclination, suggesting coplanarity. Assuming a primary mass M_* = 0.83 M_{\sun}, we obtain a companion mass M = 1.55 +/- 0.24 M_{Jup}. Given the relatively young age of epsilon Eri (~800 Myr), this accurate exoplanet mass and orbit can usefully inform future direct imaging attempts. We predict the next periastron at 2007.3 with a total separation, rho = 0.3 arcsec at position angle, p.a. = -27 degrees. Orbit orientation and geometry dictate that epsilon Eri b will appear brightest in reflected light very nearly at periastron. Radial velocities spanning over 25 years indicate an acceleration consistent with a Jupiter-mass object with a period in excess of 50 years, possibly responsible for one feature of the dust morphology, the inner cavity.