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61.
Shuichi Sato 《Integral Equations and Operator Theory》2008,62(3):429-440
We prove certain L
p
-estimates for Littlewood-Paley functions arising from rough kernels. The estimates are useful for extrapolation to prove
L
p
-boundedness of the Littlewood-Paley functions under a sharp kernel condition.
相似文献
62.
陈传淼 《数学的实践与认识》2016,(19):274-287
刘徽《割圆术》(公元263年)千古之谜被破解,发现使用了外推法,由此引发新的认识.将综述刘徽的极限和外推思想,并比较了国外的工作.最后指出如何用外推预报提出求解偏微分方程的高效算法. 相似文献
63.
64.
A well-known method of estimating the length of a parametric curve in is to sample some points from it and compute the length of the polygon passing through them. In this paper we show that for
uniform sampling of regular smooth curves, Richardson extrapolation can be applied repeatedly giving a sequence of derivative-free
length estimates of arbitrarily high orders of accuracy. A similar result is derived for the approximation of the area of
parametric surfaces.
相似文献
65.
This paper provides an error analysis for the Crank-Nicolson extrapolation scheme of time discretization applied to the spatially discrete stabilized finite element approximation of the two-dimensional time-dependent Navier-Stokes problem, where the finite element space pair for the approximation of the velocity and the pressure is constructed by the low-order finite element: the quadrilateral element or the triangle element with mesh size . Error estimates of the numerical solution to the exact solution with are derived.
66.
67.
ASYMPTOTIC ERROR EXPANSION AND DEFECT CORRECTION FOR SOBOLEV AND VISCOELASTICITY TYPE EQUATIONS 总被引:10,自引:0,他引:10
1.IntroductionLetObearectangulardomain.WeareconcernedwiththeRichardsonextrapolationanddefectcorrectionofthefiniteelementapproximationstothesolutionsofthefollowingsimpleSobolevtypeequationandviscoelasticitytypeequationTheextrapolationtechniqueusedforthefin… 相似文献
68.
In this paper we propose a fully discretized version of the collocation method applied to integral equations of the first
kind with logarithmic kernel. After a stability and convergence analysis is given, we prove the existence of an asymptotic
expansion of the error, which justifies the use of Richardson extrapolation. We further show how these expansions can be translated
to a new expansion of potentials calculated with the numerical solution of a boundary integral equation such as those treated
before. Some numerical experiments, confirming our theoretical results, are given.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
69.
J. Beeckmann R. Hesse J. Schaback H. Pitsch E. Varea N. Chaumeix 《Proceedings of the Combustion Institute》2019,37(2):1521-1528
Laminar burning velocities are of great importance in many combustion models as well as for validation and improvement of chemical kinetic schemes. Determining laminar burning velocities with high accuracy is quite challenging and different approaches exist. Hence, a comparison of existing methods measuring and evaluating laminar burning velocities is of interest. Here, two optical diagnostics, high speed tomography and Schlieren cinematography, are simultaneously set up to investigate methods for evaluating laminar flame speed in a spherical flame configuration. The hypothesis to obtain the same flame propagation radii over time with the two different techniques is addressed. Another important aspect is the estimation of flame properties, such as the unstretched flame propagation speed and Markstein length in the burnt gas phase and if these are estimated satisfactorily by common experimental approaches. Thorough evaluation of the data with several extrapolation techniques is undertaken. A systematic extrapolation approach is presented to give more confidence into results generated experimentally. The significance of the linear extrapolation routine is highlighted in this context. Measurements of spherically expanding flames are carried out in two high-pressure, high-temperature, constant-volume vessels at RWTH in Aachen, Germany and at ICARE in Orleans, France. For the discussion of the systematic extrapolation approach, flame speed measurements of methane / air mixtures with mixture Lewis numbers moderately away from unity are used. Conditions were varied from lean to rich mixtures, at temperatures of 298–373 K, and pressures of 1 atm and 5 bar. 相似文献
70.
Yixiong Yu 《声与振动》2019,53(5):237-243
Mining aeroengine operational data and developing fault diagnosis
models for aeroengines are to avoid running aeroengines under undesired conditions.
Because of the complexity of working environment and faults of aeroengines,
it is unavoidable that the monitored parameters vary widely and possess
larger noise levels. This paper reports the extrapolation of a diagnosis model
for 20 gas path faults of a double-spool turbofan civil aeroengine. By applying
support vector machine (SVM) algorithm together with genetic algorithm (GA),
the fault diagnosis model is obtained from the training set that was based on
the deviations of the monitored parameters superimposed with the noise level
of 10%. The SVM model (C = 24.7034; γ = 179.835) was extrapolated for the
samples whose noise levels were larger than 10%. The accuracies of extrapolation
for samples with the noise levels of 20% and 30% are 97% and 94%, respectively.
Compared with the models reported on the same faults, the extrapolation results
of the GASVM model are accurate. 相似文献