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 journalArticle

5 Scopus citations

Abstract

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
Volume24
Issue number5-6
DOIs
StatePublished - 1 Jan 2003

Keywords

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

Fingerprint Dive into the research topics of 'Spectral analysis of some iterations in the Chandrasekhar's H-functions'. Together they form a unique fingerprint.

  • Cite this