標題: Spectral analysis of some iterations in the Chandrasekhar's H-functions
作者: Juang, J
Lin, KY
Lin, WW
應用數學系
Department of Applied Mathematics
關鍵字: H-function;radiative transfer;nonnegative matrices;convergence;Perron-Frobenius theorem;Gauss-Jacobi;Gauss-Seidel;eigenvalues
公開日期: 1-Aug-2003
摘要: 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 'j h = (F) over tilde (h), where (F) over tilde = ((f1) over tilde, (f2) over tilde, . . . (f(n)) over tilde")(T) is a nonlinear map from R-n to R-n. Here (f(i)) over tilde = 1 /(root1 - c + Sigma(k=1)(n) (c(k)mu(k)h(k)/mu(i) + mu(k)), 0 < c less than or equal to 1, i = 1,2, . . . ,n. One such method is essentially a nonlinear Gauss-Seidel iteration with respect to (F) over tilde. The other ingenious approach is to normalize each iterate after a nonlinear Gauss-Jacobi iteration with respect to (F) over tilde 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 (root3 - 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.
URI: http://hdl.handle.net/11536/27692
ISSN: 0163-0563
期刊: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
Volume: 24
Issue: 5-6
起始頁: 575
結束頁: 586
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