3,779 research outputs found
On isolation of singular zeros of multivariate analytic systems
We give a separation bound for an isolated multiple root of a square
multivariate analytic system satisfying that an operator deduced by adding
and a projection of in a direction of the kernel of
is invertible. We prove that the deflation process applied on and this kind
of roots terminates after only one iteration. When is only given
approximately, we give a numerical criterion for isolating a cluster of zeros
of near . We also propose a lower bound of the number of roots in the
cluster.Comment: 17 page
Structure of characteristic Lyapunov vectors in spatiotemporal chaos
We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov
exponents in systems with spatiotemporal chaos. We focus on characteristic LVs
and compare the results with backward LVs obtained via successive Gram-Schmidt
orthonormalizations. Systems of a very different nature such as coupled-map
lattices and the (continuous-time) Lorenz `96 model exhibit the same features
in quantitative and qualitative terms. Additionally we propose a minimal
stochastic model that reproduces the results for chaotic systems. Our work
supports the claims about universality of our earlier results [I. G. Szendro et
al., Phys. Rev. E 76, 025202(R) (2007)] for a specific coupled-map lattice.Comment: 9 page
An inverse Sturm-Liouville problem with a fractional derivative
In this paper, we numerically investigate an inverse problem of recovering
the potential term in a fractional Sturm-Liouville problem from one spectrum.
The qualitative behaviors of the eigenvalues and eigenfunctions are discussed,
and numerical reconstructions of the potential with a Newton method from finite
spectral data are presented. Surprisingly, it allows very satisfactory
reconstructions for both smooth and discontinuous potentials, provided that the
order of fractional derivative is sufficiently away from 2.Comment: 16 pages, 6 figures, accepted for publication in Journal of
Computational Physic
- …