Linear approximation by exponential sums on finite intervals
نویسندگان
چکیده
منابع مشابه
On Approximation of Functions by Exponential Sums
We introduce a new approach, and associated algorithms, for the efficient approximation of functions and sequences by short linear combinations of exponential functions with complex-valued exponents and coefficients. These approximations are obtained for a finite but arbitrary accuracy and typically have significantly fewer terms than Fourier representations. We present several examples of thes...
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Article history: Received 15 May 2009 Accepted 15 August 2009 Available online 2 September 2009 Communicated by Ginette Saracco
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Approximations of 1/x by sums of exponentials are well studied for finite intervals. Here the error decreases like O(exp(−ck)) with the order k of the exponential sum. In this paper we investigate approximations of 1/x on the interval [1,∞). We prove estimates of the error by O(exp(−c√k)) and confirm this asymptotic estimate by numerical results. Numerical results lead to the conjecture that th...
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T -adic exponential sums associated to a Laurent polynomial f are introduced. They interpolate all classical p-power order exponential sums associated to f . The Hodge bound for the Newton polygon of L-functions of T -adic exponential sums is established. This bound enables us to determine, for all m, the Newton polygons of Lfunctions of p-power order exponential sums associated to an f which i...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1975
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1975-13779-7