Modified steepest descent method for nonlinear irregular operator equations
The author proposes a theoretic two-step iteration method for solving the nonlinear operator equation \(A(u)=f \Longleftrightarrow\) min \(\{\|A(u)-f\|^2: u\in U\}\) in a Hilbert space. The idea is based on transforming the original equation into a regularized equation and then applying a modified steepest descent method to approximate its solution. Although convergence of the proposed method is established, it is unclear how the regularization scheme should be constructed and no numerical example is given.
scientific article; zbMATH DE number 6485668