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1.
Approximation schemes for functional optimization problems with admissible solutions dependent on a large number d of variables are investigated. Suboptimal solutions are considered, expressed as linear combinations of n-tuples from a basis set of simple computational units with adjustable parameters. Different choices of basis sets are compared,
which allow one to obtain suboptimal solutions using a number n of basis functions that does not grow “fast” with the number d of variables in the admissible decision functions for a fixed desired accuracy. In these cases, one mitigates the “curse
of dimensionality,” which often makes unfeasible traditional linear approximation techniques for functional optimization problems,
when admissible solutions depend on a large number d of variables.
Marcello Sanguineti was partially supported by a PRIN grant from the Italian Ministry for University and Research (project
“Models and Algorithms for Robust Network Optimization”). 相似文献
2.
V. S. Koroliuk V. V. Koroliuk N. Limnios 《Methodology and Computing in Applied Probability》2009,11(2):201-209
We study asymptotic average and diffusion approximation schemes for semi-Markov queuing systems by a random evolution approach
and using compensating operator of the corresponding extended Markov renewal process. These results generalize Markov and
renewal flow queuing systems.
相似文献
3.
In this paper, a new numerical method for solving the optimal control of linear time-varying delay systems with quadratic
performance index is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions,
consisting of block-pulse functions and Bernoulli polynomials, are presented. The operational matrices of integration, product,
delay and the integration of the cross product of two hybrid functions of block-pulse and Bernoulli polynomials vectors are
given. These matrices are then utilized to reduce the solution of the optimal control of delay systems to the solution of
algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. 相似文献
4.
In this article, we analyze tensor approximation schemes for continuous functions. We assume that the function to be approximated lies in an isotropic Sobolev space and discuss the cost when approximating this function in the continuous analogue of the Tucker tensor format or of the tensor train format. We especially show that the cost of both approximations are dimension-robust when the Sobolev space under consideration provides appropriate dimension weights.
相似文献5.
Convergence of Iterative Difference Schemes for Two and Three Dimensional Nonlinear Parabolic Systems 下载免费PDF全文
In this paper, we study the general difference schemes of the boundary value problem for the nonlinear parabolic systems with two and three space dimensions. To solve the nonlinear difference schemes, we construct an iterative sequence from the solutions or the linearized difference schemes. We shall prove the convergence of the difference solutions for the iterative difference schemes to the solution of the original boundary value problem or the nonlinear parabolic systems. 相似文献
6.
M. Yu. Khachai E. D. Neznakhina 《Proceedings of the Steklov Institute of Mathematics》2017,297(1):97-107
A graph Γ is called a Deza graph if it is regular and the number of common neighbors of any two distinct vertices is one of two fixed values. A Deza graph is called a strictly Deza graph if it has diameter 2 and is not strongly regular. In 1992, Gardiner et al. proved that a strongly regular graph that contains a vertex with disconnected second neighborhood is a complete multipartite graph with parts of the same size greater than 2. In this paper, we study strictly Deza graphs with disconnected second neighborhoods of vertices. In Section 2, we prove that, if each vertex of a strictly Deza graph has disconnected second neighborhood, then the graph is either edge-regular or coedge-regular. In Sections 3 and 4, we consider strictly Deza graphs that contain at least one vertex with disconnected second neighborhood. In Section 3, we show that, if such a graph is edge-regular, then it is the s-coclique extension of a strongly regular graph with parameters (n, k, λ, μ), where s is an integer, s ≥ 2, and λ = μ. In Section 4, we show that, if such a graph is coedge-regular, then it is the 2-clique extension of a complete multipartite graph with parts of the same size greater than or equal to 3. 相似文献
7.
首先引入了时滞差分系统基于两种测度的极端稳定性概念,然后建立了一些关于时滞差分系统(犺0,犺)极端稳定性(极端一致稳定性,极端渐近稳定性,极端一致渐近稳定性)的判定准则.在所得到的定理中,对Δ犞的限制较弱,特别地,Δ犞甚至可以恒为正,从而便于实际应用. 相似文献
8.
9.
This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations (SDDEs) of Itô-type. The method is proved to be mean-square convergent of order min{$1/2, \hat{p}$} under the Lipschitz condition and the linear growth condition, where $\hat{p}$ is the exponent of Hölder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter $p$ the derived method can have a better stability property than more commonly used numerical methods. That is, for some $p$, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters $p$. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient. 相似文献
10.
11.
讨论了一般时间尺度上时滞脉冲系统的双测度稳定性问题.我们引进了一个新的概念即一般时间尺度上时滞脉冲系统的(h_0,h)稳定性.利用Lyapunov函数法和分析法得到了一般时间尺度上时滞脉冲系统解的双测度稳定性判据.最后给出了一个例子以说明本文结论的有效性. 相似文献
12.
Zhi-Yun Xie 《计算数学(英文版)》1990,8(3):252-260
The symplectic collocation schemes, which are based on the framework established by Feng Kang [1], are proposed for numerical solution of Hamiltonian systems. The sufficient and necessary conditions for various collocation schemes to be symplectic are obtained. Some examples of symplectic collocation schemes are also given. 相似文献
13.
E. R. Jakobsen 《BIT Numerical Mathematics》2004,44(2):269-285
In this paper we provide estimates of the rates of convergence of monotone approximation schemes for non-convex equations in one space-dimension. The equations under consideration are the degenerate elliptic Isaacs equations with x-depending coefficients, and the results applies in particular to certain finite difference methods and control schemes based on the dynamic programming principle. Recently, Krylov, Barles, and Jakobsen obtained similar estimates for convex Hamilton–Jacobi–Bellman equations in arbitrary space-dimensions. Our results are only valid in one space-dimension, but they are the first results of this type for non-convex second-order equations. 相似文献
14.
In this paper, we give sufficient conditions for the existence of (pseudo) weakly conformal and conformal families of measures for fibred systems. We describe a general construction principle for these families, modelled on the one developed by Denker and Urbanski for conformal measures. For those systems that are fibrewise local homeomorphisms, the constructed families are (pseudo) conformal. If a system is, moreover, weakly topologically exact along fibres, then each measure in the associated family is supported on the whole fibre where it is naturally defined. 相似文献
15.
If $f^{(i))}(\alpha)(\alpha=a, i=0,1,...,k-2)$ are given, then we get a class of the Hermite approximation operator Qf=F satisfying $F^{(i)}(\alpha)=f^{(i)}(\alpha)$, where F is the many-knot spline function whose knots are at points $y_i:$=$y_0$<$y_1$<$\cdots$<$y_{k-1}=b$, and $F\in P_k$ on $[y_{i-1},y_i]$. The operator is of the form $Qf:=\sum\limits_{i=0}^{k-2}[f^{(i)}(a)\phi_i+f^{(i)}(b)\psi _i]$. We give an explicit representation of $\phi_i$ and $\psi_i$ in terms of B-splines $N_{i,k}$. We show that Q reproduces appropriate classes of polynomials. 相似文献
16.
Zhi Guo WANG 《数学学报(英文版)》2007,23(7):1199-1216
We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form up to a remainder of weighted order 2d + 1. And some dynamical consequences are obtained. 相似文献
17.
In this paper, we give sufficient conditions for the existence of (pseudo) weakly conformal and conformal families of measures for fibred systems. We describe a general construction principle for these families, modelled on the one developed by Denker and Urbanski for conformal measures. For those systems that are fibrewise local homeomorphisms, the constructed families are (pseudo) conformal. If a system is, moreover, weakly topologically exact along fibres, then each measure in the associated family is supported on the whole fibre where it is naturally defined.This research was partially supported by NSF Grant DMS 0100078.Received February 4, 2002; in final form October 24, 2002
Published online October 24, 2003 相似文献
18.
We present generalized and unified families of $(2n)$-point and $(2n-1)$-point $p$-ary interpolating subdivision schemes originated from Lagrange polynomial for any integers $n ≥ 2$ and $p ≥ 3$. Almost all existing even-point and odd-point interpolating schemes of lower and higher arity belong to this family of schemes. We also present tensor product version of generalized and unified families of schemes. Moreover, error bounds between limit curves and control polygons of schemes are also calculated. It has been observed that error bounds decrease when complexity of the scheme decrease and vice versa. Furthermore, error bounds decrease with the increase of arity of the schemes. We also observe that in general the continuity of interpolating scheme do not increase by increasing complexity and arity of the scheme. 相似文献
19.
利用特征为2的有限域上射影空间,我们构作了一些三个类和4个类的结合方案,并计算了它们的参数. 相似文献
20.
Nechepurenko Yu. M. Khristichenko M. Yu. 《Computational Mathematics and Mathematical Physics》2019,59(5):731-746
Computational Mathematics and Mathematical Physics - Novel fast algorithms for computing the maximum amplification of the norm of solution and optimal disturbances for delay systems are proposed... 相似文献