Solving $L_{p}$-Norm Problems and Applications
| dc.contributor.author | Li, Yuying | en_US |
| dc.date.accessioned | 2007-04-23T16:27:52Z | |
| dc.date.available | 2007-04-23T16:27:52Z | |
| dc.date.issued | 1993-03 | en_US |
| dc.description.abstract | The $l_{p}$ norm discrete estimation problem min$_{x\in\Re^{n}} \Vert b-A^{T} x\Vert^{p}_{p}$ has been solved in many data analysis applications, e.g. geophysical modeling. Recently, a new globally convergent Newton method (called GNCS) has been proposed for solving $l{p}$ problems with 1 $\leq p \leq$ 2 [5]. This method is much faster than the widely used IRLS method when 1 $\leq p \leq$ 1.5 and comparable to it when $p greater than $ 1.5. In this paper, modification is made to the line search prodedure so that the GNCS method is applicable for $l_{p}$ problems with 1 $\leq p less than \infty$. The global convergence results for $l_{1}$ problems are obtained under weaker assumptions than required in [2]. In addition, the usefulness of $l_{p}$ norm solution with 1 $\leq p \leq$ 2 is demonstrated by applying the GNCS algorithm to a synthetic geophysical tomographic inversion problem. Additional numerical results are included to support the efficiency of GNCS. Key Words: linear regression, discrete estimation, tomographic inversion, IRLS, GNCS, linear programming, Newton method. Subject Classification: AMS/MOS: 65H10, 65K05, 65K10. | en_US |
| dc.format.extent | 1681044 bytes | |
| dc.format.extent | 514005 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.format.mimetype | application/postscript | |
| dc.identifier.citation | http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR93-1331 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1813/6097 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Cornell University | en_US |
| dc.subject | computer science | en_US |
| dc.subject | technical report | en_US |
| dc.title | Solving $L_{p}$-Norm Problems and Applications | en_US |
| dc.type | technical report | en_US |