29,892 research outputs found
Iterative Solution of the Supereigenvalue Model
An integral form of the discrete superloop equations for the supereigenvalue
model of Alvarez-Gaume, Itoyama, Manes and Zadra is given. By a change of
variables from coupling constants to moments we find a compact form of the
planar solution for general potentials. In this framework an iterative scheme
for the calculation of higher genera contributions to the free energy and the
multi-loop correlators is developed. We present explicit results for genus one.Comment: 21 pages, LaTeX, no figure
Iterative solution of perturbation equations
Iterative solution of perturbation equation
A Systematic Extended Iterative Solution for QCD
An outline is given of an extended perturbative solution of Euclidean QCD
which systematically accounts for a class of nonperturbative effects, while
allowing renormalization by the perturbative counterterms. Proper vertices
Gamma are approximated by a double sequence Gamma[r,p], with r the degree of
rational approximation w.r.t. the QCD mass scale Lambda, nonanalytic in the
coupling g, and p the order of perturbative corrections in g-squared,
calculated from Gamma[r,0] - rather than from the perturbative Feynman rules
Gamma(0)(pert) - as a starting point. The mechanism allowing the
nonperturbative terms to reproduce themselves in the Dyson-Schwinger equations
preserves perturbative renormalizability and is tied to the divergence
structure of the theory. As a result, it restricts the self-consistency problem
for the Gamma[r,0] rigorously - i.e. without decoupling approximations - to the
superficially divergent vertices. An interesting aspect of the scheme is that
rational-function sequences for the propagators allow subsequences describing
short-lived excitations. The method is calculational, in that it allows known
techniques of loop computation to be used while dealing with integrands of
truly nonperturbative content.Comment: 48 pages (figures included). Scope of replacement: correction of a
technical defect; no changes in conten
Preconditioned iterative solution of the 2D Helmholtz equation
Using a finite element method to solve the Helmholtz equation leads to a sparse system of equations which in three dimensions is too large to solve directly. It is also non-Hermitian and highly indefinite and consequently difficult to solve iteratively. The approach taken in this paper is to precondition this linear system with a new preconditioner and then solve it iteratively using a Krylov subspace method. Numerical analysis shows the preconditioner to be effective on a simple 1D test problem, and results are presented showing considerable convergence acceleration for a number of different Krylov methods for more complex problems in 2D, as well as for the more general problem of harmonic disturbances to a non-stagnant steady flow
Variational-Iterative Solution of Ground State for Central Potential
The newly developed iterative method based on Green function defined by
quadratures along a single trajectory is combined with the variational method
to solve the ground state quantum wave function for central potentials. As an
example, the method is applied to discuss the ground state solution of Yukawa
potential, using Hulthen solution as the trial function.Comment: 9 pages with 1 tabl
Iterative solution of a discrete axially symmetric potential problem
The Dirichlet problem for the axially symmetric potential equation in a cylindrical domain is discretized by means of a five-point difference approximation. The resulting difference equation is solved by point or line iterative methods. The rate of convergence of these methods is determined by the spectral radius of the underlying point or line Jacobi matrix. An asymptotic approximation for this spectral radius, valid for small mesh size, is derived
- …