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Applications of structured total lea...

Zhang, Lei.

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Applications of structured total least norm method.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Applications of structured total least norm method./
作者:	Zhang, Lei.
面頁冊數:	74 p.
附註:	Advisers: Haesun Park; J. Ben Rosen.
Contained By:	Dissertation Abstracts International62-03B.
標題:	Computer Science. -
電子資源:	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.
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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.
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790 1 0 $a Rosen, J. Ben, $e advisor
791 $a Ph.D.
792 $a 2001
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