Geodesic
Probability against condition number and sampling of multivariate trigonometric random polynomials
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 178-189.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The difficult factor in the condition number of a large linear system is the $\textcent $###$\sterling $###$\textcent $###$\textcent $###$\sterling \ddot $§$\copyright \textcent \sterling $ spectral norm of . To eliminate this factor, we here replace worst case analysis by a probabilistic argument. To $\sterling $###§$\copyright $be more precise, we randomly take from a ball with the uniform distribution and show that then, with a certain probability close to one, the relative errors and satisfy with a constant that involves $\textcent $###$\textcent \textcent $###$ !\textcent \textcent $###$\textcent $#"% textcent$###$ !textcentonly the Frobenius and spectral norms of . The success of this argument is demonstrated for Toeplitz systems and £for the problem of sampling multivariate trigonometric polynomials on nonuniform knots. The limitations of the argument are also shown.
Classification : 65F35, 15A12, 47B35, 60H25, 94A20
Keywords: condition number, probability argument, linear system, Toeplitz matrix, nonuniform sampling, multivariate trigonometric polynomial 
@article{ETNA_2007__26__a16,
     author = {B\"ottcher, Albrecht and Potts, Daniel},
     title = {Probability against condition number and sampling of multivariate trigonometric random polynomials},
     journal = {Electronic transactions on numerical analysis},
     pages = {178--189},
     publisher = {mathdoc},
     volume = {26},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a16/}
}
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Böttcher, Albrecht; Potts, Daniel. Probability against condition number and sampling of multivariate trigonometric random polynomials. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 178-189. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a16/