1,246 research outputs found
The -weighted dual programming of the linear Chebyshev approximation and an interior-point method
Given samples of a real or complex-valued function on a set of distinct
nodes, the traditional linear Chebyshev approximation is to compute the best
minimax approximation on a prescribed linear functional space. Lawson's
iteration is a classical and well-known method for that task. However, Lawson's
iteration converges linearly and in many cases, the convergence is very slow.
In this paper, by the duality theory of linear programming, we first provide an
elementary and self-contained proof for the well-known Alternation Theorem in
the real case. Also, relying upon the Lagrange duality, we further establish an
-weighted dual programming for the linear Chebyshev approximation. In this
framework, we revisit the convergence of Lawson's iteration, and moreover,
propose a Newton type iteration, the interior-point method, to solve the
-weighted dual programming. Numerical experiments are reported to
demonstrate its fast convergence and its capability in finding the reference
points that characterize the unique minimax approximation.Comment: 29 pages, 8 figure
Lifshitz Scaling Effects on Holographic Superconductors
Via numerical and analytical methods, the effects of the Lifshitz dynamical
exponent on holographic superconductors are studied in some detail,
including wave and wave models. Working in the probe limit, we find
that the behaviors of holographic models indeed depend on concrete value of
. We obtain the condensation and conductivity in both Lifshitz black hole
and soliton backgrounds with general . For both wave and wave models
in the black hole backgrounds, as increases, the phase transition becomes
more difficult and the growth of conductivity is suppressed. For the Lifshitz
soliton backgrounds, when increases (), the critical chemical
potential decreases in the wave cases but increases in the wave cases.
For wave models in both Lifshitz black hole and soliton backgrounds, the
anisotropy between the AC conductivity in different spatial directions is
suppressed when increases. The analytical results uphold the numerical
results.Comment: Typos corrected; Footnote added; References added; To be published in
Nuclear Physics
Federated Primal Dual Fixed Point Algorithm
Federated learning (FL) is a distributed learning paradigm that allows
several clients to learn a global model without sharing their private data. In
this paper, we generalize a primal dual fixed point (PDFP) \cite{PDFP} method
to federated learning setting and propose an algorithm called Federated PDFP
(FPDFP) for solving composite optimization problems. In addition, a
quantization scheme is applied to reduce the communication overhead during the
learning process. An convergence rate (where is the
communication round) of the proposed FPDFP is provided. Numerical experiments,
including graph-guided logistic regression, 3D Computed Tomography (CT)
reconstruction are considered to evaluate the proposed algorithm.Comment: 29 pages and 8 figure
Lifshitz effects on holographic -wave superfluid
In the probe limit, we numerically build a holographic -wave superfluid
model in the four-dimensional Lifshitz black hole coupled to a Maxwell-complex
vector field. We observe the rich phase structure and find that the Lifshitz
dynamical exponent contributes evidently to the effective mass of the
matter field and dimension of the gravitational background. Concretely, we
obtain the Cave of Winds appeared only in the five-dimensional anti-de
Sitter~(AdS) spacetime, and the increasing hinders not only the condensate
but also the appearance of the first-order phase transition. Furthermore, our
results agree with the Ginzburg-Landau results near the critical temperature.
In addition, the previous AdS superfluid model is generalized to the Lifshitz
spacetime.Comment: 14 pages,5 figures, and 1 table, accepted by Phys. Lett.
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