8,926 research outputs found
An Elimination Method for Solving Bivariate Polynomial Systems: Eliminating the Usual Drawbacks
We present an exact and complete algorithm to isolate the real solutions of a
zero-dimensional bivariate polynomial system. The proposed algorithm
constitutes an elimination method which improves upon existing approaches in a
number of points. First, the amount of purely symbolic operations is
significantly reduced, that is, only resultant computation and square-free
factorization is still needed. Second, our algorithm neither assumes generic
position of the input system nor demands for any change of the coordinate
system. The latter is due to a novel inclusion predicate to certify that a
certain region is isolating for a solution. Our implementation exploits
graphics hardware to expedite the resultant computation. Furthermore, we
integrate a number of filtering techniques to improve the overall performance.
Efficiency of the proposed method is proven by a comparison of our
implementation with two state-of-the-art implementations, that is, LPG and
Maple's isolate. For a series of challenging benchmark instances, experiments
show that our implementation outperforms both contestants.Comment: 16 pages with appendix, 1 figure, submitted to ALENEX 201
An Exact Algorithm for Any-flavor Lattice QCD with Kogut-Susskind Fermion
We propose an exact simulation algorithm for lattice QCD with dynamical
Kogut-Susskind fermion in which the N_f-flavor fermion operator is defined as
the N_f/4-th root of the Kogut-Susskind (KS) fermion operator. The algorithm is
an extension of the Polynomial Hybrid Monte Carlo (PHMC) algorithm to KS
fermions. The fractional power of the KS fermion operator is approximated with
a Hermitian Chebyshev polynomial, with which we can construct an algorithm for
any number of flavors. The error which arises from the approximation is
corrected by the Kennedy-Kuti noisy Metropolis test. Numerical simulations are
performed for the two-flavor case for several lattice parameters in order to
confirm the validity and the practical feasibility of the algorithm. In
particular tests on a 16^4 lattice with a quark mass corresponding to
m_{PS}/m_V ~ 0.68 are successfully accomplished. We conclude that our algorithm
provides an attractive exact method for dynamical QCD simulations with KS
fermions.Comment: 35 pages, 12 figures, uses elsart.cls, v2: typos corrected,
comparison to the R-algorithm on large size lattice is adde
Efficient computation of TM- and TE-polarized leaky modes in multilayered circular waveguides
In combination with the perfectly matched layer (PML)-paradigm, eigenmode expansion techniques have become increasingly important in the analysis and design of cylindrical and planar waveguides for photonics applications. To achieve high accuracy, these techniques rely on the determination of many modes of the modal spectrum of the waveguide under consideration. In this paper, we focus on the efficient computation of TM- and TE-polarized leaky modes for multilayered cylindrical waveguides. First, quasi-static estimates are derived for the propagation constants of these modes. Second, these estimates are used as a starting point in an advanced Newton iteration scheme after they have been subjected to an adaptive linear error correction. To prove the validity of the computation technique, it is applied to technologically important cases: vertical-cavity surface-emitting lasers and a monomode fiber
An Algorithm for Gluinos on the Lattice
L\"uscher's local bosonic algorithm for Monte Carlo simulations of quantum
field theories with fermions is applied to the simulation of a possibly
supersymmetric Yang-Mills theory with a Majorana fermion in the adjoint
representation. Combined with a correction step in a two-step polynomial
approximation scheme, the obtained algorithm seems to be promising and could be
competitive with more conventional algorithms based on discretized classical
(``molecular dynamics'') equations of motion. The application of the considered
polynomial approximation scheme to optimized hopping parameter expansions is
also discussed.Comment: latex2e, 23 pages, 4 figures with epsfig. Section 5 is rewritten,
more data are added and the discussion is extende
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