690 research outputs found
Simulation-efficient marginal posterior estimation with <i>swyft</i>:Stop wasting your precious time
Spectral cutoffs in indirect dark matter searches
Indirect searches for dark matter annihilation or decay products in the
cosmic-ray spectrum are plagued by the question of how to disentangle a dark
matter signal from the omnipresent astrophysical background. One of the
practically background-free smoking-gun signatures for dark matter would be the
observation of a sharp cutoff or a pronounced bump in the gamma-ray energy
spectrum. Such features are generically produced in many dark matter models by
internal Bremsstrahlung, and they can be treated in a similar manner as the
traditionally looked-for gamma-ray lines. Here, we discuss prospects for seeing
such features with present and future Atmospheric Cherenkov Telescopes.Comment: 4 pages, 2 figures, 1 table; conference proceedings for TAUP 2011,
Munich 5-9 Se
Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962
- 968 (2003)] introduced in connection with the summation of the divergent
perturbation expansion of the hydrogen atom in an external magnetic field a new
sequence transformation which uses as input data not only the elements of a
sequence of partial sums, but also explicit estimates
for the truncation errors. The explicit
incorporation of the information contained in the truncation error estimates
makes this and related transformations potentially much more powerful than for
instance Pad\'{e} approximants. Special cases of the new transformation are
sequence transformations introduced by Levin [Int. J. Comput. Math. B
\textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189
- 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and
also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A
\textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations
- explicit expressions, recurrence formulas, explicit expressions in the case
of special remainder estimates, and asymptotic order estimates satisfied by
rational approximants to power series - is formulated in terms of hitherto
unknown mathematical properties of the new transformation introduced by
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable
formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of
Mathematical Physic
Resummation of QED Perturbation Series by Sequence Transformations and the Prediction of Perturbative Coefficients
We propose a method for the resummation of divergent perturbative expansions in quantum electrodynamics and related field theories. The method is based on a nonlinear sequence transformation and uses as input data only the numerical values of a finite number of perturbative coefficients. The results obtained in this way are for alternating series superior to those obtained using Padé approximants. The nonlinear sequence transformation fulfills an accuracy-through-order relation and can be used to predict perturbative coefficients. In many cases, these predictions are closer to available analytic results than predictions obtained using the Padé method
An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions
This paper sketches a technique for improving the rate of convergence of a
general oscillatory sequence, and then applies this series acceleration
algorithm to the polylogarithm and the Hurwitz zeta function. As such, it may
be taken as an extension of the techniques given by Borwein's "An efficient
algorithm for computing the Riemann zeta function", to more general series. The
algorithm provides a rapid means of evaluating Li_s(z) for general values of
complex s and the region of complex z values given by |z^2/(z-1)|<4.
Alternatively, the Hurwitz zeta can be very rapidly evaluated by means of an
Euler-Maclaurin series. The polylogarithm and the Hurwitz zeta are related, in
that two evaluations of the one can be used to obtain a value of the other;
thus, either algorithm can be used to evaluate either function. The
Euler-Maclaurin series is a clear performance winner for the Hurwitz zeta,
while the Borwein algorithm is superior for evaluating the polylogarithm in the
kidney-shaped region. Both algorithms are superior to the simple Taylor's
series or direct summation.
The primary, concrete result of this paper is an algorithm allows the
exploration of the Hurwitz zeta in the critical strip, where fast algorithms
are otherwise unavailable. A discussion of the monodromy group of the
polylogarithm is included.Comment: 37 pages, 6 graphs, 14 full-color phase plots. v3: Added discussion
of a fast Hurwitz algorithm; expanded development of the monodromy
v4:Correction and clarifiction of monodrom
Acceleration of generalized hypergeometric functions through precise remainder asymptotics
We express the asymptotics of the remainders of the partial sums {s_n} of the
generalized hypergeometric function q+1_F_q through an inverse power series z^n
n^l \sum_k c_k/n^k, where the exponent l and the asymptotic coefficients {c_k}
may be recursively computed to any desired order from the hypergeometric
parameters and argument. From this we derive a new series acceleration
technique that can be applied to any such function, even with complex
parameters and at the branch point z=1. For moderate parameters (up to
approximately ten) a C implementation at fixed precision is very effective at
computing these functions; for larger parameters an implementation in higher
than machine precision would be needed. Even for larger parameters, however,
our C implementation is able to correctly determine whether or not it has
converged; and when it converges, its estimate of its error is accurate.Comment: 36 pages, 6 figures, LaTeX2e. Fixed sign error in Eq. (2.28), added
several references, added comparison to other methods, and added discussion
of recursion stabilit
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