臺灣博碩士論文加值系統

為了要解決一系列的矩陣 Riccati 方程式,我們提供了四種疊代的技巧,
分別是 Gauss-Jacobi, Gauss-Seidel, JOR, SOR 等方法; 其中方程式內
包含兩個重要變數 C 和 α。C 和 α 均為介於 0,1 間之實數。C代表粒
子每次碰撞後發生散射的比例,而 α 代表角度之改變量。此一系列方程
式是從所謂 "簡單轉移模式" 而來,並滿足線性粒子轉移之反射矩陣。本
論文的目的是在於分析 C 和 α 對於疊代解之收歛速率的影響,此外我們
並要比較 Gauss-Jacobi 和 Gauss-Seidel 兩種方法在解決此一問題時的
收歛速率。

We provide four iterative techniques the Gauss-Jacobi,eidel,
JOR, and SOR methods for solving a certain class of algebraic
matrix Riccati equations with two parameters, C ( 0≦C≦1 ) and
α ( 0≦α≦1 ). Here C denotes then of scattering per
collision, and α is an angular shift. Equations of this class
are induced, via invariant imbedding and the shifted Gauss-
Legendre quadrature formula, from a "simple-transport model"
and are satisfied by the reflection matrix for linear particle
transport in a half- space. The purpose of this paper is to
describe the effects of the parameters C and α on the
convergence rates of the iterative solutions. We also compare
the convergence rates of the Gauss-Jacobi and Gauss-Seidel
methods.