1986/12/01 by A. R. DiDonato, Alfred H. Morris · 2 citations
Computer Science · Mathematics · #Numerical Methods and Algorithms #Iterative Methods for Nonlinear Equations #Mathematical and Theoretical Analysis #Computation #Mathematics #Applied mathematics #Inverse #Function (biology) #Algorithm #Newton's method #Set (abstract data type) #Incomplete gamma function #Gamma function #Mathematical analysis #Computer science #Physics
paper · pdf · doi:10.1145/22721.23109
openalex publication_date 1986/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An algorithm is given for computing the incomplete gamma function ratios P ( a , x ) and Q> ( a , x ) for a ⪈ 0, x ⪈ 0, a + x ≠ 0. Temme's uniform asymptotic expansions are used. The algorithm is robust; results accurate to 14 significant digits can be obtained. An' extensive set of coefficients for the Temme expansions is included. An algorithm, employing third-order Schröder iteration supported by Newton-Raphson iteration, is provided for computing x when a , P ( a , x ), and Q ( a , x ) are given. Three iterations at most are required to obtain 10 significant digit accuracy for x .