The Centroid Decomposition and Other Approximations to the SVD

摘要0204157 Funderlic，Robert E.北卡罗来纳州本节总结了在NSF赠款DMS-9804759的支持下，共同主要研究者所取得的进展（07/01/98 06/30/00），用于自适应光学应用的自适应控制算法和DMS-0073056项目（08/01/00 7/31/03）对于前者的矩阵构造逆问题的算法项目，目标是设计，分析，和评估自适应控制算法foradaptive光学应用。PI为自适应光学中的线性构造器问题建立了一个数学框架，并在对延迟-延迟控制算法的理解方面取得了进展。本论文的目的是研究从规定的光谱数据中构造以矩阵形式描述的物理模型的理论和实践。本论文收集、艾德和定义了本征值反问题的整体概念，并发展了一些新的数值方法来处理一些逆特征值问题。到目前为止，在NSF的支持下，这些目标的一个重要部分已经完成，如下所示。

ABSTRACT 0204157Funderlic, Robert E.North Carolina State UThis section summarizes the progress the co-PI has made under the support of NSF grants DMS-9804759(07/01/98 06/30/00)for the project Adaptive Control Algorithm for Adaptive Optics Applications andDMS-0073056 (08/01/00 7/31/03)for the project Algorithms for the Inverse Problem of Matrix Con-struction of the former,the objectives are to design,analyze,and evaluate adaptive control algorithms foradaptive optics applications.The co-PI has established a mathematical framework for the linear econstructorproblem in adaptive optics,and has made progress in the understanding of a latency-delay control algorithm.Fo the latter,the proposed objectives were to investigate both the theory and the practice of constructing aphysical model,described mathematically in the form of a matrix,from prescribed spectral data.The co-PIhas collected,classi .ed,and de .ned the egimen of inverse eigenvalue problems as a whole,and has developednew numerical methods for tackling some inverse eigenvalue problems.Thus far,a signi .cant portion of theseobjectives has been accomplished under the NSF support as is evidenced below.