The Centroid Decomposition and Other Approximations to the SVD

摘要 0204157Funderlic, Robert E.北卡罗来纳州立大学本节总结了联合 PI 在 NSF 拨款 DMS-9804759 (07/01/98 06/30/00) 项目“自适应光学应用的自适应控制算法”和 DMS-0073056 (08/01/00 7/31/03) 的支持下取得的进展前者的矩阵构造逆问题算法项目，目标是设计、分析和评估自适应光学应用的自适应控制算法。共同PI建立了自适应光学中线性构造问题的数学框架，并在理解延迟控制算法方面取得了进展。对于后者，提出的目标是研究构造物理模型的理论和实践，以数学形式描述共同PI已经从整体上收集、分类和定义了反特征值问题的本征，并开发了新的数值方法来解决一些反特征值问题。到目前为止，这些目标的很大一部分已经在NSF的支持下完成，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.