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151.
S. Yu. Sovetnikova G. V. Khromova 《Computational Mathematics and Mathematical Physics》2007,47(4):555-563
The zero-order Tikhonov regularization method as applied to an equation of the first kind with a multiple differentiation operator is considered for the case when the solution belongs to a class from the domain of the adjoint operator. An estimate of the error of the approximate solution in the uniform metric is obtained, which is sharp with respect to the order, and the order is established. It is proved that the proposed method is optimal with respect to the order. Unimprovable estimates of the order of the modulus of continuity of the inverse operator are obtained. 相似文献
152.
This paper presents an error analysis for classification algorithms generated by regularization schemes with polynomial kernels.
Explicit convergence rates are provided for support vector machine (SVM) soft margin classifiers. The misclassification error
can be estimated by the sum of sample error and regularization error. The main difficulty for studying algorithms with polynomial
kernels is the regularization error which involves deeply the degrees of the kernel polynomials. Here we overcome this difficulty
by bounding the reproducing kernel Hilbert space norm of Durrmeyer operators, and estimating the rate of approximation by
Durrmeyer operators in a weighted L1 space (the weight is a probability distribution). Our study shows that the regularization parameter should decrease exponentially
fast with the sample size, which is a special feature of polynomial kernels.
Dedicated to Charlie Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 68T05, 62J02.
Ding-Xuan Zhou: The first author is supported partially by the Research Grants Council of Hong Kong (Project No. CityU 103704). 相似文献
153.
The alignment correlation term in the β-decay angular distribution from purely nuclear spin aligned 20Na has been measured for the first time. The final objective is to test the G parity symmetry, one of the fundamental symmetry in the weak nucleon current. For artificial creation of the alignment, the
knowledge of the hyperfine interaction of 20Na implanted in a single-crystal ZnO was utilized.
*Research Abroad, Japan Society for the Promotion of Science 相似文献
154.
Yuzuru Eguchi 《国际流体数值方法杂志》2003,41(8):881-904
A new regularization method is proposed for the Galerkin approximation of the incompressible Navier–Stokes equations with Q1/P0 element, by newly introducing a square‐type linear form into the variational divergence‐free constraint regularized with the global pressure jump (GPJ) method. The addition of the square‐type linear form is intended to eliminate the hydrostatic pressure mode appearing in confined flows, and to make the discretized matrix positive definite and then non‐singular without the pressure pegging trick. Effects of the free parameters for the regularization on the solutions are numerically examined with a 2‐D driven cavity flow problem. Furthermore, the convergences in the conjugate gradient iteration for the solution of the pressure Poisson equation are compared among the mixed method, the GPJ method and the present method for both leaky and non‐leaky 3‐D driven cavity flows. Finally, the non‐leaky 3‐D cavity flows at different Re numbers are solved to compare with the literature data and to demonstrate the accuracy of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
155.
Nguyen Buong 《Computational Mathematics and Mathematical Physics》2007,47(10):1583-1588
The goal of this study is to analyze the Tikhonov regularization method as applied to a general nonlinear optimization problem
that has been previously reduced to an unconstrained optimization problem. The stability properties of the method are examined,
and its convergence is proved.
The text was submitted by the author in English. 相似文献
156.
Marius Ghergu 《Journal of Mathematical Analysis and Applications》2007,333(1):265-273
We are concerned with singular elliptic equations of the form −Δu=p(x)(g(u)+f(u)+a|∇u|) in RN (N?3), where p is a positive weight and 0<a<1. Under the hypothesis that f is a nondecreasing function with sublinear growth and g is decreasing and unbounded around the origin, we establish the existence of a ground state solution vanishing at infinity. Our arguments rely essentially on the maximum principle. 相似文献
157.
We study the maximal term of the Hadamard composition of Dirichlet series with real exponents. We obtain a lower estimate for the sum of a Dirichlet series over a curve arbitrarily approaching the convergence line. 相似文献
158.
无简并微扰论公式的研究 总被引:2,自引:0,他引:2
本文介绍了Wigner公式,Goldstone公式与Schrodinger公式及其递推形式,比较表明,Schrodinger公式的递推形式更容易利用计算机程序实现。文中还给出了逐级计算非连通项到任意级的方法。 相似文献
159.
160.
本文推广了Tikhonov正则化方法,导出了带复数核的第一类Fredholm积分方程的正则解应满足的正则积分微分方程,并讨论了正则解的收敛性·作为这一方法的应用,数值求解了与二维摇板造波问题相应的一类逆问题,并给出了选择最佳正则参数的一个实用的方法 相似文献