共查询到20条相似文献,搜索用时 15 毫秒
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We consider a statistical inverse learning (also called inverse regression) problem, where we observe the image of a function f through a linear operator A at i.i.d. random design points \(X_i\), superposed with an additive noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimation of Af) and the inverse (estimation of f) learning problems. In this general framework, we obtain strong and weak minimax optimal rates of convergence (as the number of observations n grows large) for a large class of spectral regularization methods over regularity classes defined through appropriate source conditions. This improves on or completes previous results obtained in related settings. The optimality of the obtained rates is shown not only in the exponent in n but also in the explicit dependency of the constant factor in the variance of the noise and the radius of the source condition set. 相似文献
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Mediterranean Journal of Mathematics - In the present paper, we prove a global inverse theorem for approximation of bounded continuous functions on the interval [0, ∞) by linear combinations... 相似文献
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本文对推广的Kantorovich多项式算子,在满足一定条件下,得出了算子逼近过程中的一个整体逆定理,从而推广了文献[1]中Z.Ditzian的结果. 相似文献
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R. P. Agarwal M. Balaj D. O’Regan 《Journal of Optimization Theory and Applications》2012,155(2):417-429
The purpose of this paper is to present a unified approach to study the existence of solutions for two types of variational relation problems, which encompass several generalized equilibrium problems, variational inequalities and variational inclusions investigated in the recent literature. By using two well-known fixed point theorems, we establish several existence criteria for the solutions of these problems. 相似文献
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本文从严格的数学分析的思想方法,研究了无穷级数中的狄尼定理,指出它的逆命题是不成立的,同时也给出了反例.后半部分在引用一个引理的基础上,证明了正项级数∑∞n=1an/rαnrβn-1也收敛,即将狄尼定理适当进行推广. 相似文献
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M.H.Farag 《计算数学(英文版)》2004,22(5):633-640
This paper presents the stability of difference approximations of an optimal control problem for a quasilinear parabolic equation with controls in the coefficients, boundary conditions and additional restrictions. The optimal control problem has been convered to one of the optimization problem using a penalty function technique. The difference approximations problem for the considered problem is obtained. The estimations of stability of the solution of difference approximations problem are proved. The stability estimation of the solution of difference approximations problem by the controls is obtained. 相似文献
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We obtain a necessary and sufficient condition for a given collection of elements to freely generate a free associative algebra. We present some necessary conditions for primitivity of an element of a free associative algebra of rank 2. 相似文献
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在工业生产中,随着员工操作技能的熟练程度的增加,对于相同的任务越往后加工,所花的时间将会减少。 同时,为了尽早完工,管理者也会考虑给加工工件分配一定量的额外资源来缩短工件加工时间。 本文基于以上实例,讨论了工件的实际加工时间既具有学习效应又依赖所分配资源的单机排序问题。 在问题中,假设工件的学习效应是之前已加工工件正常加工时间和的指数函数。 同时随着分配给工件资源量的增加,工件的实际加工时间呈线性减少,所需费用呈线性增加。对这一排序模型,主要探讨以下五个目标函数:最小化最大完工时间与资源消耗量总费用的和;最小化总完工时间与资源消耗量总费用的和;最小化加权总完工时间与资源消耗量总费用的和;最小化总提前、总延误、总共同交货期与资源消耗量总费用的和以及最小化总提前、总延误、总松弛交货期与资源消耗量总费用的和。 本文对前三个目标函数相应的排序问题给出了多项式时间可求解的算法。 对后两个目标函数所涉及的排序问题借助于指派问题分别给出了时间复杂性为O(n3)的算法。 相似文献
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Mediterranean Journal of Mathematics - The inversion problem for a given polynomial set, $${\{P_n\}_{n\geq0}}$$ , expanded in a basis $${\{\mathfrak{B}_{n}\}}$$ is the problem of finding the... 相似文献
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《Mathematische Nachrichten》1989,141(1):325-334
The determination of variable filtration through a layer is an important and actual problem in filtration theory. This problem has been examined in some particular cases, for instance in the papers [1, 2]. 相似文献
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Ren-Cang Li 《计算数学(英文版)》1992,10(2):97-111
Two new algorithms based on QR decompositions (QRDs) (with column pivoting) are proposed for solving inverse eigenvalue problems, and under some non-singularity assumptions they are both locally quadratically convergent. Several numerical tests are presented to illustrate their convergence behavior. 相似文献
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讨论热传导方程求解系数的一个反问题.把问题归结为一个非线性不适定的算子方程后,考虑该方程的Newton型迭代方法.对线性化后的Newton方程用隐式迭代法求解,关键的一步是引入了一种新的更合理的确定(内)迭代步数的后验准则.对新方法及对照的Tikhonov方法和Bakushiskii方法进行了数值实验,结果显示了新方法具有明显的优越性. 相似文献
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Gabriele Bonanno 《Journal of Global Optimization》2004,28(3-4):249-258
The existence of two intervals of positive real parameters λ for which the functional Φ + λΨ has three critical points, whose norms are uniformly bounded in respect to λ belonging to one of the two intervals, is established. As an example of an application to nonlinear differential problems, a two point boundary value problem is considered and multiplicity results are obtained. 相似文献
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Abstract We prove a global Inverse Map Theorem for a map f from the Heisenberg group into itself, provided the Pansu differential of f is continuous, non singular and satisfies some growth conditions at infinity. An estimate for the Lipschitz constant (with
respect to the Carnot–Carathéodory distance in
) of a continuously Pansu differentiable map is included. This gives a characterization of (continuously Pansu differentiable)
globally biLipscitz deformations of
in term of a pointwise estimate of their differential.
Keywords: Inverse problem, Heisenberg group 相似文献