Nonlinear Kolmogorov widths |
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Authors: | V. N. Temlyakov |
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Affiliation: | (1) Department of Mathematics, University of South Carolina, Columbia;(2) V. A. Steklov Mathematics Institute, USSR |
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Abstract: | We investigate a generalization of width in the sense of Kolmogorov suitable for estimating bestm-term approximations. We generalize Carl's inequality which gives lower estimate of Kolmogorov widths in terms of entropy numbers. Application of these new inequalities gives some progress in the problem of estimating bestm-term trigonometric approximations of multivariate functions.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 891–902, June, 1998.This research was supported by the National Science Foundation under grant No. DMS 9622925 and by the ONR foundation under grant No. N00014-96-1-1003. |
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Keywords: | entropy nonlinear approximation Kolmogorov width |
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