Accuracy and Precision of Algorithms for Bessel Functions of First Kind and Integer Order

Abstract

Abstract : Three different algorithms--the power series, the asymptotic series, and the recurrence relation method--are investigated with special attention to the single (10 to the -14th power) and double precision (10 to the -29th power) of CDC 6000 Series computers. The final accuracy of each method depends partly on the magnitudes of the largest and smallest terms when floating point additions are involved. Another consideration is the number of terms required for each algorithm. Combination of all considerations leads to a partitioning of the order-argument domain into partially overlapping areas in which each algorithm is most appropriate. A wedged area not covered by any of the algorithms remains for large order and argument of approximately equal size. Orders and arguments up to 1024 were investigated and checked where possible. A FORTRAN IV program in the form of an external function is included.