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161.
This paper concerns the cubic smoothing spline approach to nonparametric regression. After first deriving sharp asymptotic formulas for the eigenvalues of the smoothing matrix, the paper uses these formulas to investigate the efficiency of different selection criteria for choosing the smoothing parameter. Special attention is paid to the generalized maximum likelihood (GML), C
p
and extended exponential (EE) criteria and their marginal Bayesian interpretation. It is shown that (a) when the Bayesian model that motivates GML is true, using C
p
to estimate the smoothing parameter would result in a loss of efficiency with a factor of 10/3, proving and strengthening a conjecture proposed in Stein (1990); (b) when the data indeed come from the C
p
density, using GML would result in a loss of efficiency of ; (c) the loss of efficiency of the EE criterion is at most 1.543 when the data are sampled from its consistent density family. The paper not only studies equally spaced observations (the setting of Stein, 1990), but also investigates general sampling scheme of the design points, and shows that the efficiency results remain the same in both cases.This work is supported in part by NSF grant DMS-0204674 and Harvard University Clark-Cooke Fund.
Mathematics Subject Classification (2000):Primary: 62G08; Secondary: 62G20 相似文献
162.
Tong Yang Huijiang Zhao Changjiang Zhu 《Proceedings of the American Mathematical Society》2003,131(4):1257-1266
We give uniform BV estimates and -stability of Lax-Friedrichs' scheme for a class of systems of strictly hyperbolic conservation laws whose integral curves of the eigenvector fields are straight lines, i.e., Temple class, under the assumption of small total variation. This implies that the approximate solutions generated via the Lax-Friedrichs' scheme converge to the solution given by the method of vanishing viscosity or the Godunov scheme, and then the Glimm scheme or the wave front tracking method.
163.
We solve a linear parabolic equation in d , d 1, with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the -method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes. 相似文献
164.
Michel Hébert 《Applied Categorical Structures》2001,9(6):595-623
We give concrete versions of the characterizations of locally -presentable (resp. -generated) categories as categories of models of (resp. weakly) -ary limit-theories and of (resp. weakly) -ary essentially algebraic theories. By concrete we mean that starting with a category of -structures, the theories obtained are extensions of the original ones, and the equivalences of categories are concrete isomorphisms. -presentable and -generated objects are also investigated from this viewpoint. 相似文献
165.
On the basis of the experimental reports, the mechanism of the second-order susceptibility (2) for the thermal/electric field poling of fused silica is analyzed, and expressions for (2) are detailedly derived and numerically calculated for the first time. By comparison the theoretical value of (2) with the experiment results, we propose that the effective (2) is created via both the interaction of the intense electric field with the third-order susceptibility (3) and the dipole orientation. The theoretical results show that, in the differently applied voltage, the dipole orientation and (3) play different role in the formation of (2). This theory successfully explains some experiment results. 相似文献
166.
S. A. Kuzhel 《Mathematical Notes》2000,68(5-6):724-729
The paper presents some necessary and sufficient conditions on abstract positive self-adjoint operators L under which the operator-differential equation
determines a free evolution in the Lax--Phillips scattering scheme. 相似文献
167.
Let V and W be n-dimensional vector spaces over GF(2). A function Q : V W is called crooked (a notion introduced by Bending and Fon-Der-Flaass) if it satisfies the following three properties:
We show that crooked functions can be used to construct distance regular graphs with parameters of a Kasami distance regular graph, symmetric 5-class association schemes similar to those recently constructed by de Caen and van Dam from Kasami graphs, and uniformly packed codes with the same parameters as the double error-correcting BCH codes and Preparata codes. 相似文献
168.
This paper deals with the iterative solution of stage equations which arise when some fully implicit Runge-Kutta methods,
in particular those based on Gauss, Radau and Lobatto points, are applied to stiff ordinary differential equations. The error
behaviour in the iterates generated by Newton-type and, particularly, by single-Newton schemes which are proposed for the
solution of stage equations is studied. We consider stiff systems y'(t) = f(t,y(t)) which are dissipative with respect to
a scalar product and satisfy a condition on the relative variation of the Jacobian of f(t,y) with respect to y, similar to
the condition considered by van Dorsselaer and Spijker in [7] and [17]. We prove new convergence results for the single-Newton
iteration and derive estimates of the iteration error that are independent of the stiffness. Finally, some numerical experiments
which confirm the theoretical results are presented.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
169.
170.
A second-order accurate numerical method for the two-dimensional fractional diffusion equation 总被引:1,自引:0,他引:1
Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. In this paper, we present an accurate and efficient numerical method to solve a fractional superdiffusive differential equation. This numerical method combines the alternating directions implicit (ADI) approach with a Crank–Nicolson discretization and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method. The stability and the consistency of the method are established. Numerical solutions for an example super-diffusion equation with a known analytic solution are obtained and the behavior of the errors are analyzed to demonstrate the order of convergence of the method. 相似文献