Spectral analysis of some iterations in the Chandrasekhar's H-functions

Juang Jonq*, Kun Yi Lin, Wen-Wei Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 ki + 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.

Original languageEnglish
Pages (from-to)575-586
Number of pages12
JournalNumerical Functional Analysis and Optimization
Issue number5-6
StatePublished - 1 Jan 2003


  • Convergence
  • Eigenvalues
  • Gauss-Jacobi
  • Gauss-Seidel
  • H-function
  • Nonnegative matrices
  • Perron-Frobenius theorem
  • Radiative transfer

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