无界算子线性方程的迭代求解

无界算子的迭代算子分裂方法：误差分析与实例

Iterative operator-splitting methods for unbounded operators: Error analysis and examples

本文提出并分析了一种针对无界算子的迭代算子分裂方法，推导了误差界，并应用于双曲和抛物型方程以及薛定谔方程。

Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain

We consider the Cauchy problem for the Helmholtz equation with a domain in R^d, d>2 with N cylindrical outlets to infinity with bounded inclusions in R^{d-1}. Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Maz'ya proposed an alternating iterative method for solving Cauchy problems associated with elliptic,self-adjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We cons…

基于不精确数据的无界算子最优恢复

On optimal recovery of unbounded operators from inaccurate data

研究不精确数据下无界算子的最优恢复，证明截断方法在特定条件下可达到最高精度与最少离散信息的最优值，并以数值微分和倒向抛物方程为例验证。

无界算子的分裂方法

Splitting methods for unbounded operators

本文研究在向量场及其分量可能无界时将其分裂为三个分量的计算方法，通过替代方法推导出在无界算子存在时仍有效的误差表达式和误差界。

无界算子不适定问题的正则化

Regularization of Ill-Posed Problems with Unbounded Operators

针对无界闭算子（可能非线性），论证了变分正则化和拟解方法的合理性，并给出了简洁的一般性结果。