2,051,862 research outputs found
Approximation systems
We introduce the notion of an approximation system as a generalization of
Taylor approximation, and we give some first examples. Next we develop the
general theory, including error bounds and a sufficient criterion for
convergence. More examples follow. We conclude the article with a description
of numerical implementation and directions for future research. Prerequisites
are mostly elementary complex analysis.Comment: 27 pages; in v3 minor change
Approximation Schemes for Partitioning: Convex Decomposition and Surface Approximation
We revisit two NP-hard geometric partitioning problems - convex decomposition
and surface approximation. Building on recent developments in geometric
separators, we present quasi-polynomial time algorithms for these problems with
improved approximation guarantees.Comment: 21 pages, 6 figure
Approximation Theory XV: San Antonio 2016
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22\u201325, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type.
The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation
Extended Limber Approximation
We develop a systematic derivation for the Limber approximation to the
angular cross-power spectrum of two random fields, as a series expansion in
1/(\ell+1/2). This extended Limber approximation can be used to test the
accuracy of the Limber approximation and to improve the rate of convergence at
large \ell's. We show that the error in ordinary Limber approximation is
O(1/\ell^2). We also provide a simple expression for the second order
correction to the Limber formula, which improves the accuracy to O(1/\ell^4).
This correction can be especially useful for narrow redshift bins, or samples
with small redshift overlap, for which the zeroth order Limber formula has a
large error. We also point out that using \ell instead of (\ell+1/2), as is
often done in the literature, spoils the accuracy of the approximation to
O(1/\ell).Comment: 7 pages, 6 figure
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