保守和角移半平面的反射矩陣之收斂加速方法

Abstract

考慮代數矩陣的Riccati方程式，它有兩個參數，分別為c和.alpha.，讓 如此的非線性方程以F(S)=0來表示，這□的F是一個非線性的映射。在這 篇論文，首先讓S^*是F(S)=0的最小正解，我們證明了F^'(S^*)是奇異的 在 c=1和.alpha.=0的時候。再來就是對於奇異和非常靠近奇異的問題， 我們有使它們加速的方法，而且有非常滿意的數值結果。 Consider a class of algebraic matrix Riccati equation with two parameters c and .alpha..Let such class of nonlinear be denoted by F(S)=0,in which F is a nonlinear map.In thesis,we first show F^'(S^*) is singular for c=1 and .alpha.=0.Here S^* is the minimal positive solution of F(S)=0.Second,certain procedures are proposed for the singular problem and nearms. Some very satisfactory numerical results are also presented.