Solution of Structured Total Least Norm and Parameter Estimation Problems

在科学和工程的许多重要应用中，都需要对数据矩阵和目标向量都可能存在误差的超定线性系统进行求解。最近，一种被称为结构化总最小范数（STLN）的新技术被开发出来，用于在数据被扰动以解释误差后获得保留任何仿射结构的解。它还允许在各种规范下误差最小。STLN算法正在被研究并发展成为一种高效实用的求解方法。它的计算性能正在研究中，更完整的收敛理论正在发展中。为了有效地处理大规模问题和特殊结构，正在进行重大的算法和改进。将STLN方法应用于汉克尔范数逼近问题的模型约简进行了研究。人们正在探索不同规范的影响。STLN算法正在得到扩展，以解决更一般的问题，其中结构化矩阵是待估计参数的可微函数，并将其性能与其他参数估计方法（如proony方法）进行比较。

A solution to an over determined linear system, where there may be errors in both the data matrix and the target vector, is required in many important applications in sciences and engineering. Recently, a new technique called Structured Total Least Norm (STLN) has been developed for obtaining the solution that preserves any affine structure, after the data are perturbed to account for the errors. It also permits the error to be minimized in various norms. The STLN algorithm is being investigated and developed into an efficient and practical solution method for many applications. Its computational performance is being studied and a more complete convergence theory is under development. Significant algorithmic and improvements are being made in order to efficiently handle large-scale problems and special structures. A particular study is being conducted to apply the STLN method to the model reduction by Hankel norm approximation problem. The effect of different norms are being explored. The STLN algorithm is being extended to solve more general problems where the structured matrix is a differentiable function of parameters to be estimated, and its performance is to be compared to other parameter estimation methods such as Prony's method.