6,887 research outputs found
Spin polarizabilities and polarizabilities of the nucleon studied by free and quasi-free Compton scattering at MAMI (Mainz)
In addition to the E2/M1 ratio of the N-> transition, the
electromagnetic polarizabilities and spin-polarizabilities are important
structure constants of the nucleon which serve as sensitive tests of chiral
perturbation theory and of models of the nucleon. Recently, these quantities
have been investigated experimentally at MAMI (Mainz) by high-precision Compton
scattering using hydrogen and deuterium targets, where for the latter the
method of quasi-free scattering has been applied.Comment: Proceedings of GDH 2002, Genova, Italy 3-6 July 2002 (updated
version
A New Algorithm for Computing the Actions of Trigonometric and Hyperbolic Matrix Functions
A new algorithm is derived for computing the actions and
, where is cosine, sinc, sine, hyperbolic cosine, hyperbolic
sinc, or hyperbolic sine function. is an matrix and is
with . denotes any matrix square root of
and it is never required to be computed. The algorithm offers six independent
output options given , , , and a tolerance. For each option, actions
of a pair of trigonometric or hyperbolic matrix functions are simultaneously
computed. The algorithm scales the matrix down by a positive integer ,
approximates by a truncated Taylor series, and finally uses the
recurrences of the Chebyshev polynomials of the first and second kind to
recover . The selection of the scaling parameter and the degree of
Taylor polynomial are based on a forward error analysis and a sequence of the
form in such a way the overall computational cost of the
algorithm is optimized. Shifting is used where applicable as a preprocessing
step to reduce the scaling parameter. The algorithm works for any matrix
and its computational cost is dominated by the formation of products of
with matrices that could take advantage of the implementation of
level-3 BLAS. Our numerical experiments show that the new algorithm behaves in
a forward stable fashion and in most problems outperforms the existing
algorithms in terms of CPU time, computational cost, and accuracy.Comment: 4 figures, 16 page
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