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收集所有交通大學研究人員與學生個人或團體所發表之各項學術著作，涵蓋期刊論文、教師專書、學位論文等項。;;Collections of Publications of NCTU Researchers and Students Like Journal Papers and Thesis.

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🏛️國立陽明交通大學機構典藏

Author: search.filters.author.Lin, WWSubject: search.filters.subject.nonnegative matrices

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Now showing 1 - 3 of 3
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    Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices
    (1998-09-22)
    Juang, J
    ;
    Lin, WW
    ;
    應用數學系
    ;
    Department of Applied Mathematics
    We consider a nonsymmetric algebraic matrix Riccati equation arising from transport theory. The nonnegative solutions of the equation can be explicitly constructed via the inversion formula of a Cauchy matrix. An error analysis and numerical results are given. We also show a comparison theorem of the nonnegative solutions.
  • Thumbnail Image
    Item type:Item,
    Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices
    (1998-09-22)
    Juang, J
    ;
    Lin, WW
    ;
    應用數學系
    ;
    Department of Applied Mathematics
    We consider a nonsymmetric algebraic matrix Riccati equation arising from transport theory. The nonnegative solutions of the equation can be explicitly constructed via the inversion formula of a Cauchy matrix. An error analysis and numerical results are given. We also show a comparison theorem of the nonnegative solutions.
  • Thumbnail Image
    Item type:Item,
    Spectral analysis of some iterations in the Chandrasekhar's H-functions
    (2003-08-01)
    Juang, J
    ;
    Lin, KY
    ;
    Lin, WW
    ;
    應用數學系
    ;
    Department of Applied Mathematics
    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.