动力系统方法解决无界线性算子方程

Dynamical Systems Method for Solving Linear Unbound Operator Equations

针对反问题中出现的第一类算子方程Au=f,其中A是实Hilbert空间H上的一个无界线性算子利用动力系统方法和正则化方法,求解上述问题的正则化问题的解：u＇（t）=-A~＊（Au（t）-f）利用线性算子半群理论可以得到上述正则化问题的解的半群表示,并证明了当t→∞时,所得的正则化解收敛于原问题的解.

On studying the first kind of operator equation Au=f in the inverse problems, A is an unbounded linear operator in the real Hilbert space H. Using the methods of dynamical systems and regulaxization method, the regularization equation u＇ （t） = -A＊ （Au （t） - f） of the problem has been solved. With linear operator semigroup theory, we get the solution of the regularization equation, and prove that the regularized solution converged to the solution of the original problem when t→∞.