Matrix Algorithm for the Computation of Zeros of Nonnegative Order Bessel Functions

Abstract

Consider the problem of computing a given number N of the smallest positive zeros j_<ν, 1>・・・, j_<ν, N> of Bessel function j_ν(z) of a given nonnegative order ν with a given relative accurasy ε > 0. In this paper, we describe how to implement our matrix algorithm developed earlier for this purpose for the case 0 ≤ ν ≤ 30, ε ≥ 10^<-24> and N ≤ 15. The algorithm can be extended to the case where ν is negative. However, if ν is close to a negative integer then the problem turns out to be ill-conditioned.