The Centroid Decomposition and Other Approximations to the SVD

摘要0204157北卡罗来纳州州立大学罗伯特·E·范德里克这一部分总结了在美国国家科学基金会拨款的支持下，联合PI所取得的进展DMS-9804759(07/01/98 06/30/00)用于自适应光学应用的自适应控制算法项目和DMS-0073056(08/01/00 7/31/03)对于前者的矩阵构造逆问题的项目算法，目标是设计、分析和评估用于自适应光学应用的自适应控制算法。联合PI为自适应光学中的线性经济结构问题建立了一个数学框架，对于后者，提出的目标是研究从规定的频谱数据建立以矩阵形式数学描述的物理模型的理论和实践。合作PI收集、分类和归纳了整个逆特征值问题的范例，并发展了解决一些逆特征值问题的新的数值方法。到目前为止，在NSF的支持下，这些目标中的很大一部分已经完成，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.