525 research outputs found
Can Computer Algebra be Liberated from its Algebraic Yoke ?
So far, the scope of computer algebra has been needlessly restricted to exact
algebraic methods. Its possible extension to approximate analytical methods is
discussed. The entangled roles of functional analysis and symbolic programming,
especially the functional and transformational paradigms, are put forward. In
the future, algebraic algorithms could constitute the core of extended symbolic
manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure
Decoding of Interleaved Reed-Solomon Codes Using Improved Power Decoding
We propose a new partial decoding algorithm for -interleaved Reed--Solomon
(IRS) codes that can decode, with high probability, a random error of relative
weight at all code rates , in time polynomial in the
code length . For , this is an asymptotic improvement over the previous
state-of-the-art for all rates, and the first improvement for in the
last years. The method combines collaborative decoding of IRS codes with
power decoding up to the Johnson radius.Comment: 5 pages, accepted at IEEE International Symposium on Information
Theory 201
A semi analytic iterative method for solving two forms of blasius equation / Mat Salim Selamat, Nurul Atkah Halmi and Nur Azyyati Ayob
In this paper, a semi analytic iterative method (SAIM) is presented for solving two forms of Blasius equation. Blasius equation is a third order nonlinear ordinary differential equation in the problem of the two-dimensional laminar viscous flow over half-infinite domain. In this scheme, the first solution which is in a form of convergent series solution is combined with Padé approximants to handle the boundary condition at infinity. Comparison the results obtained by SAIM with those obtained by other method such as variational iteration method and differential transform method revealed the effectiveness of the SAIM
Spectral properties from Matsubara Green's function approach - application to molecules
We present results for many-body perturbation theory for the one-body Green's
function at finite temperatures using the Matsubara formalism. Our method
relies on the accurate representation of the single-particle states in standard
Gaussian basis sets, allowing to efficiently compute, among other observables,
quasiparticle energies and Dyson orbitals of atoms and molecules. In
particular, we challenge the second-order treatment of the Coulomb interaction
by benchmarking its accuracy for a well-established test set of small
molecules, which includes also systems where the usual Hartree-Fock treatment
encounters difficulties. We discuss different schemes how to extract
quasiparticle properties and assess their range of applicability. With an
accurate solution and compact representation, our method is an ideal starting
point to study electron dynamics in time-resolved experiments by the
propagation of the Kadanoff-Baym equations.Comment: 12 pages, 8 figure
- …