A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD Method
A new technique to find the optimization parameter in TSVD regularization method is based on a curve which is drawn against the residual norm [5]. Since the TSVD regularization is a method with discrete regularization parameter, then the above-mentioned curve is also discrete. In this paper we prese...
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| Format: | Article |
| Language: | fas |
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Kharazmi University
2015-07-01
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| Series: | پژوهشهای ریاضی |
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| Online Access: | http://mmr.khu.ac.ir/article-1-2530-en.html |
| _version_ | 1797871736111235072 |
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| author | A.R. Keshvari S.M Hosseni |
| author_facet | A.R. Keshvari S.M Hosseni |
| author_sort | A.R. Keshvari |
| collection | DOAJ |
| description | A new technique to find the optimization parameter in TSVD regularization method is based on a curve which is drawn against the residual norm [5]. Since the TSVD regularization is a method with discrete regularization parameter, then the above-mentioned curve is also discrete. In this paper we present a mathematical analysis of this curve, showing that the curve has L-shaped path very similar to that of the classical L-curve and its corner point can represent the optimization regularization parameter very well. In order to find the corner point of the L-curve (optimization parameter), two methods are applied: pruning and triangle. Numerical results show that in the considered test problems the new curve is better than the classical L-curve. |
| first_indexed | 2024-04-10T00:47:21Z |
| format | Article |
| id | doaj.art-86d4327519de4f348fe4dd6e018c1428 |
| institution | Directory Open Access Journal |
| issn | 2588-2546 2588-2554 |
| language | fas |
| last_indexed | 2024-04-10T00:47:21Z |
| publishDate | 2015-07-01 |
| publisher | Kharazmi University |
| record_format | Article |
| series | پژوهشهای ریاضی |
| spelling | doaj.art-86d4327519de4f348fe4dd6e018c14282023-03-13T19:17:56ZfasKharazmi Universityپژوهشهای ریاضی2588-25462588-25542015-07-01117584A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD MethodA.R. Keshvari0S.M Hosseni1 Department of Mathematical Sciences, Sistan and Baluchestan University Department of Mathematical Sciences, Sistan and Baluchestan University A new technique to find the optimization parameter in TSVD regularization method is based on a curve which is drawn against the residual norm [5]. Since the TSVD regularization is a method with discrete regularization parameter, then the above-mentioned curve is also discrete. In this paper we present a mathematical analysis of this curve, showing that the curve has L-shaped path very similar to that of the classical L-curve and its corner point can represent the optimization regularization parameter very well. In order to find the corner point of the L-curve (optimization parameter), two methods are applied: pruning and triangle. Numerical results show that in the considered test problems the new curve is better than the classical L-curve.http://mmr.khu.ac.ir/article-1-2530-en.htmltsvd regularizationdiscrete l-curvenew l-curve |
| spellingShingle | A.R. Keshvari S.M Hosseni A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD Method پژوهشهای ریاضی tsvd regularization discrete l-curve new l-curve |
| title | A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD Method |
| title_full | A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD Method |
| title_fullStr | A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD Method |
| title_full_unstemmed | A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD Method |
| title_short | A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD Method |
| title_sort | mathematical analysis of new l curve to estimate the parameters of regularization in tsvd method |
| topic | tsvd regularization discrete l-curve new l-curve |
| url | http://mmr.khu.ac.ir/article-1-2530-en.html |
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