4,422 research outputs found
Univariate interpolation by exponential functions and gaussian RBFs for generic sets of nodes
We consider interpolation of univariate functions on arbitrary sets of nodes
by Gaussian radial basis functions or by exponential functions. We derive
closed-form expressions for the interpolation error based on the
Harish-Chandra-Itzykson-Zuber formula. We then prove the exponential
convergence of interpolation for functions analytic in a sufficiently large
domain. As an application, we prove the global exponential convergence of
optimization by expected improvement for such functions.Comment: Some stylistic improvements and added references following feedback
from the reviewer
Effects of Smoothing Functions in Cosmological Counts-in-Cells Analysis
A method of counts-in-cells analysis of galaxy distribution is investigated
with arbitrary smoothing functions in obtaining the galaxy counts. We explore
the possiblity of optimizing the smoothing function, considering a series of
-weight Epanechnikov kernels. The popular top-hat and Gaussian smoothing
functions are two special cases in this series. In this paper, we mainly
consider the second moments of counts-in-cells as a first step. We analytically
derive the covariance matrix among different smoothing scales of cells, taking
into account possible overlaps between cells. We find that the Epanechnikov
kernel of is better than top-hat and Gaussian smoothing functions in
estimating cosmological parameters. As an example, we estimate expected
parameter bounds which comes only from the analysis of second moments of galaxy
distributions in a survey which is similar to the Sloan Digital Sky Survey.Comment: 33 pages, 10 figures, accepted for publication in PASJ (Vol.59, No.1
in press
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