Partially Structured Matrices and Numerically Reliable Displacement Algorithms

摘要

Many problems in linear prediction, signal processing digital filtering and in several other areas can be formulated in terms of structured matrices and their inverses. Most of the algorithms which respect the structure in Matrices suffer from propagation of round-off errors. Hence all the prevalent mathematical software tools explore structure ignoring methods. We studied the problem of designing fast and numerically accurate algorithms which respect the partial structure in matrices. We also studied the problem of extending and applying the structured matrix computations to problems in H infinity filtering, inverse scattering, adaptive filtering and recursive updates. We also looked into the development of robust estimation schemes for data fusion scenarios and to study the performance limits of several adaptive schemes. We have also studied how structured matrix factorizations can be used to develop new structures for sub-band adaptive filtering. The mixed H sub 2/H infinity approach to controller design is an attempt to incorporate optimal performance and guarantee robustness, arguably the two most desirable properties, into a single controller. The robust performance problem formulated in the mixed H sub 2/H infinity framework largely remains an open problem. In this study. using a number of ideas from convex optimization theory, we have developed an efficient numerical approach to design fixed order mixed controller. In another study. we looked into the problem of designing equalizers for communication channels from an H infinity point of view.