The Centroid Decomposition and Other Approximations to the SVD

本节总结了在美国国家科学基金资助项目DMS-9804759（07/01/98 06/30/00）和dms -0073056（08/01/00 7/31/03）的支持下，共同项目在自适应光学应用的自适应控制算法的设计、分析和评估方面所取得的进展。co-PI为自适应光学中的线性构造问题建立了数学框架，并在理解延迟-延迟控制算法方面取得了进展。对于后者，提出的目标是研究从规定的光谱数据中以矩阵的形式进行数学描述的物理模型的理论和实践。co- pi收集了，经典的。Ed和de。从整体上研究了特征值反问题的解法，并对一些特征值反问题提出了新的数值求解方法。到目前为止，在美国国家科学基金会的支持下，这些目标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.