Two very general, fast and simple iterative methods were proposed by Bosma and de Rooij (Bosma, P. B., de Rooij, W. A. (1983). Efficient methods to calculate Chandrasekhar's H functions. Astron. Astrophys. 126:283-292.) to determine Chandrasekhar's H-functions. The methods are based on the use of the equation h = F̃(h), where F̃ = (f̃1, f̃ 2,...,f̃n)T is a nonlinear map from R n to Rn. Here f̃i = 1/(√1-c + ∑k=1n (ckμkh k/μi + μk)), 0 < c ≤ 1, i = 1,2,...,n. One such method is essentially a nonlinear Gauss-Seidel iteration with respect to F̃. The other ingenious approach is to normalize each iterate after a nonlinear Gauss-Jacobi iteration with respect to F̃ is taken. The purpose of this article is two-fold. First, we prove that both methods converge locally. Moreover, the convergence rate of the second iterative method is shown to be strictly less than (√3 - 1)/2. Second, we show that both the Gauss-Jacobi method and Gauss-Seidel method with respect to some other known alternative forms of the Chandrasekhar's H-functions either do not converge or essentially stall for c = 1.