Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Regularised synthesis of the magnetic field using the L-curve approach

Regularised synthesis of the magnetic field using the L-curve approach Ill-posed problems occur frequently in science and engineering. Regularisation methods are used for computing stable solutions to the ill-posed problems. The purpose of regularisation is to incorporate more information about the desired solution in order to stabilise the problem and find a useful and stable solution. The most common and well-known form of regularisation is that of Tikhonov in which the regularised solution is searched as a minimizer of the weighted combination of the residual norm and a side constraint. The weight given to the minimisation of the side constraint is controlled by the regularisation parameter. Thus, the regularisation parameter is an important factor that controls the quality of the regularised solution. A good regularisation parameter should fairly balance the perturbation error and the regularisation error in the regularised solution. There are several methods for choosing regularisation parameter. In the paper we demonstrate another method: the L-curve criterion for choosing the regularisation parameter. The L-curve is a plot of the seminorm of the regularised solution versus the corresponding residual norm thus expressing the compromise between minimisation of these two terms. The L-curve method efficiency is demonstrated on examples of synthesis of magnetic field of different kind. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Applied Electromagnetics and Mechanics IOS Press

Regularised synthesis of the magnetic field using the L-curve approach

Download PDF
10 pages

Loading next page...
 
/lp/ios-press/regularised-synthesis-of-the-magnetic-field-using-the-l-curve-approach-kp0Mcyp2sd

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
IOS Press
Copyright
Copyright © 2005 by IOS Press, Inc
ISSN
1383-5416
eISSN
1875-8800
Publisher site
See Article on Publisher Site

Abstract

Ill-posed problems occur frequently in science and engineering. Regularisation methods are used for computing stable solutions to the ill-posed problems. The purpose of regularisation is to incorporate more information about the desired solution in order to stabilise the problem and find a useful and stable solution. The most common and well-known form of regularisation is that of Tikhonov in which the regularised solution is searched as a minimizer of the weighted combination of the residual norm and a side constraint. The weight given to the minimisation of the side constraint is controlled by the regularisation parameter. Thus, the regularisation parameter is an important factor that controls the quality of the regularised solution. A good regularisation parameter should fairly balance the perturbation error and the regularisation error in the regularised solution. There are several methods for choosing regularisation parameter. In the paper we demonstrate another method: the L-curve criterion for choosing the regularisation parameter. The L-curve is a plot of the seminorm of the regularised solution versus the corresponding residual norm thus expressing the compromise between minimisation of these two terms. The L-curve method efficiency is demonstrated on examples of synthesis of magnetic field of different kind.

Journal

International Journal of Applied Electromagnetics and Mechanics – IOS Press

Published: Jan 1, 2005

There are no references for this article.