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Regularization methods for inverse p...

Orozco Rodriguez, Jose Alberto.

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Regularization methods for inverse problems.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Regularization methods for inverse problems./
Author:	Orozco Rodriguez, Jose Alberto.
Description:	91 p.
Notes:	Source: Dissertation Abstracts International, Volume: 72-06, Section: B, page: .
Contained By:	Dissertation Abstracts International72-06B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3449161
ISBN:	9781124556758

Regularization methods for inverse problems.
Orozco Rodriguez, Jose Alberto.

Regularization methods for inverse problems. - 91 p.

Source: Dissertation Abstracts International, Volume: 72-06, Section: B, page: .

Thesis (Ph.D.)--University of Minnesota, 2011.

Many applications in industry and science require the solution of an inverse problem. To obtain a stable estimate of the solution of such problems, it is often necessary to implement a regularization strategy. In the first part of the present work, a multiplicative regularization strategy is analyzed and compared with Tikhonov regularization. In the second part, an inverse problem that arises in financial mathematics is analyzed and its solution is regularized.

ISBN: 9781124556758Subjects--Topical Terms:

1669109
Applied Mathematics.

Regularization methods for inverse problems.
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020 $a 9781124556758
035 $a (UMI)AAI3449161
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100 1 $a Orozco Rodriguez, Jose Alberto. $3 1685459
245 1 0 $a Regularization methods for inverse problems.
300 $a 91 p.
500 $a Source: Dissertation Abstracts International, Volume: 72-06, Section: B, page: .
500 $a Adviser: Fadil Santosa.
502 $a Thesis (Ph.D.)--University of Minnesota, 2011.
520 $a Many applications in industry and science require the solution of an inverse problem. To obtain a stable estimate of the solution of such problems, it is often necessary to implement a regularization strategy. In the first part of the present work, a multiplicative regularization strategy is analyzed and compared with Tikhonov regularization. In the second part, an inverse problem that arises in financial mathematics is analyzed and its solution is regularized.
520 $a Tikhonov regularization for the solution of discrete ill-posed problems is well documented in the literature. The L-curve criterion is one of a few techniques that are preferred for the selection of the Tikhonov parameter. A more recent regularization approach less well known is a multiplicative regularization strategy, which unlike Tikhonov regularization, does not require the selection of a parameter. We analyze a multiplicative regularization strategy for the solution of discrete ill-posed problems by comparing it with Tikhonov regularization aided with the L-curve criterion.
520 $a We then proceed to analyze the stability of a method for estimating the risk-neutral density (RND) for the price of an asset from option prices. RND estimation is an inverse problem. The method analyzed first applies the principle of maximum entropy, where the maximum entropy solution (MES) corresponds to the estimated RND. Next, it provides an effective characterization of the constraint qualification (CQ) under which the MES can be computed by solving the dual problem, where an explicit function in finitely many variables is minimized. In our analysis, we show that the MES is stable under parameter perturbation, but the parameters are unstable under data perturbation. When noisy data are used, we show how to project the data so that the CQ is satisfied and the method can be used. To stabilize the method, we use Tikhonov regularization and choose the penalty parameter via the L-curve method. We demonstrate with numerical examples that the method becomes then much more stable to perturbation in data. Accordingly, we perform a convergence analysis of the regularized solution
590 $a School code: 0130.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
690 $a 0364
690 $a 0405
710 2 $a University of Minnesota. $b Mathematics. $3 1675975
773 0 $t Dissertation Abstracts International $g 72-06B.
790 1 0 $a Santosa, Fadil, $e advisor
790 1 0 $a Adams, Scot $e committee member
790 1 0 $a Lerman, Gilad $e committee member
790 1 0 $a Qiu, Peihua $e committee member
790 $a 0130
791 $a Ph.D.
792 $a 2011
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3449161