在再生核空间中方程AuBu+Cu=f的求解方法  

THE METHODS FOR SOLVING THE EQUATION AuBu + Cu = f

作　　者：李春利[1] 崔明根[1] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《高等学校计算数学学报》2003年第2期102-109,共8页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1 引言 本文研究下面一类非线性算子方程求解问题AuBu+Cu＝f, (1.1)其中f,u∈W(Ω),u(0)＝1,‖f‖＝1,A,B,C∈L(W(Ω)→W(Ω)),L(W(Ω)→ W(Ω))是W(Ω)到W(Ω)的连续线性算子空间,W(Ω)是定义在Ω域上的(Ω是实数域R的有界域)再生核空间.We first study the problem of solving continuous linear operator equations in separable Hilbert space. The necessary and sufficient condition for the existence and the uniqueness of solution of the equation is given. We give also minimal norm solution of the equation. Using above methods, we give the factorization method and the characteristic value method for solving the nonlinear operator equation AuBu + Cu =f. Some examples are also given for illustrating this theory.

关 键 词：再生核空间 非线性算子方程 解法 连续线性算子方程 Hilbert空间 投影算子 最小范数解 正交基 因式分解法 特征值法 

分 类 号：O241.6[理学—计算数学] O177.1[理学—数学]