Polynomial approximations to integral transforms
نویسندگان
چکیده
منابع مشابه
On Polynomial Approximations to AC
We make progress on some questions related to polynomial approximations of AC0. It is known, by works of Tarui (Theoret. Comput. Sci. 1993) and Beigel, Reingold, and Spielman (Proc. 6th CCC 1991), that any AC0 circuit of size s and depth d has an ε-error probabilistic polynomial over the reals of degree (log(s/ε))O(d). We improve this upper bound to (log s)O(d) · log(1/ε), which is much better ...
متن کاملPolynomial Approximations to Bessel Functions
A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order have similar accuracies.
متن کاملHenstock-Kurzweil Integral Transforms
Copyright q 2012 Salvador Sánchez-Perales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show conditions for the existence, continuity, and differentiability of functions defined by ΓΓs ∞ −∞ ftgt, sdt, where f is a func...
متن کاملIntegral approximations to π with nonnegative integrands
Since the integrand is nonnegative on the interval [0, 1], this shows that π is strictly less than 22/7, the well known approximation to π. Here we shall look at some features of this integral, including error bounds and a related series expansion. Then, we present a number of generalizations, including a new series approximation to π where each term adds as many digits of accuracy as you wish....
متن کاملOn Polynomial Approximations to AC^0
In this talk, we will discuss some questions related to polynomial approximations of AC0. A classic result due to Tarui (1991) and Beigel, Reingold, and Spielman (1991), states that any AC0 circuit of size s and depth d has an -error probabilistic polynomial over the reals of degree at most (log(s/))ˆ{O(d)}. We will have a re-look at this construction and show how to improve the bound to (log s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1961
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-61-99221-3