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Applications of structured total lea...

Zhang, Lei.

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Applications of structured total least norm method.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Applications of structured total least norm method./
Author:	Zhang, Lei.
Description:	74 p.
Notes:	Advisers: Haesun Park; J. Ben Rosen.
Contained By:	Dissertation Abstracts International62-03B.
Subject:	Computer Science. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3010596
ISBN:	0493201327

Applications of structured total least norm method.
Zhang, Lei.

Applications of structured total least norm method. - 74 p.

Advisers: Haesun Park; J. Ben Rosen.

Thesis (Ph.D.)--University of Minnesota, 2001.

Both theoretical justification and computational testing show that STLN and SNTLN are efficient methods for solving structured overdetermined systems. In this paper, we further extend these methods to solve some very important problems.

ISBN: 0493201327Subjects--Topical Terms:

626642
Computer Science.

Applications of structured total least norm method.
LDR:03272nam 2200325 a 45 001 932970
005 20110505
008 110505s2001 eng d
020 $a 0493201327
035 $a (UnM)AAI3010596
035 $a AAI3010596
040 $a UnM $c UnM
100 1 $a Zhang, Lei. $3 931553
245 1 0 $a Applications of structured total least norm method.
300 $a 74 p.
500 $a Advisers: Haesun Park; J. Ben Rosen.
500 $a Source: Dissertation Abstracts International, Volume: 62-03, Section: B, page: 1473.
502 $a Thesis (Ph.D.)--University of Minnesota, 2001.
520 $a Both theoretical justification and computational testing show that STLN and SNTLN are efficient methods for solving structured overdetermined systems. In this paper, we further extend these methods to solve some very important problems.
520 $a Finally, we discuss the extraordinary robustness of <italic>L</italic> 1 norm approximation.
520 $a A new algorithm called Structured Total Least Norm (STLN) has recently been developed for obtaining an approximate solution to the structured overdetermined linear system. The STLN algorithm can be extended to solve the more difficult structured overdetermined nonlinear system. This extension is called Structured Nonlinear Total Least Norm (SNTLN).
520 $a We first study a kernel problem in NMR spectroscopy: parameter and model order estimation of a sum of <italic>K</italic> exponentially damped sinusoids embedded in noise. Two most commonly used methods are the Kumaresan-Tufts' linear prediction (LP) method and the HSVD method. Those two methods constitute the so called black-box methods: they require no prior knowledge. However, it is known that when some of the noise components are large, i.e., the SNR is small, these methods may break down. We show how SNTLN can be applied to this problem, and by imposing prior knowledge on the model parameters, which causes the Cramer-Rao (CR) bounds to decrease and lowers the threshold SNR, how it can significantly improve the results. This is verified by the performance comparison of the SNTLN-based method with that of the HSVD and the LP methods.
520 $a Secondly, we consider the structure preserving rank reduction problem which arises in many important applications. The singular value decomposition (SVD), while giving the best low rank approximation to a given matrix, may not be appropriate for these applications since it does not preserve the given structure. We present a new STLN-based method for structure preserving low rank approximation of a matrix. An algorithm is described for Hankel structure preserving low rank approximation using STLN with <italic>Lp</italic> norm. Computational results are presented, which compare the performance of the STLN based method for <italic>L</italic>1 and <italic>L</italic> 2 norms and other existing methods for reduced rank approximation of Hankel matrices.
590 $a School code: 0130.
650 4 $a Computer Science. $3 626642
690 $a 0984
710 2 0 $a University of Minnesota. $3 676231
773 0 $t Dissertation Abstracts International $g 62-03B.
790 $a 0130
790 1 0 $a Park, Haesun, $e advisor
790 1 0 $a Rosen, J. Ben, $e advisor
791 $a Ph.D.
792 $a 2001
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3010596