共查询到17条相似文献,搜索用时 171 毫秒
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提出了一种多项式泛函网络运算新模型,来求解任意数域或环上多项式运算问题。同时给出了基于泛函网络求任意一元多项式倍式的学习算法,而网络的参数利用解线性方程组方法来完成。实验结果表明,这种神经计算方法,相对传统方法,不但能够获得问题的精确解,而且可获得问题的近似解。这给工程计算软件的二次开发提供了有效方法。 相似文献
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层次泛函网络整体学习算法 总被引:12,自引:1,他引:11
文中设计了一类单输人单输出泛函网络与双输人单输出泛函网络作为构造层次泛函网络基本模型,提出了一种层次泛函网络模型,给出了层次泛函网络构造方法和整体学习算法,而层次泛函网络的参数利用解方程组来进行逐层学习.以非线性代数方程组为例,指出人们熟知的一些数学解题方法可以用层次泛函网络来表达,探讨了基于层次泛函网络求解非线性代数方程组学习算法实现的一些技术问题.相对传统方法,层次泛函网络更适合于具有层次结构的应用领域.计算机仿真结果表明,这种层次学习方法具有较快的收敛速度和良好的逼近性能. 相似文献
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Banach压缩映射原理不仅在泛函分析中占有举足轻重的地位,同时也是数值分析中求解代数方程、常微分方程解存在唯一性,以及数学分析中积分方程求解的重要理论依据。它是数学和工程计算中最常用的方法之一。基于Banach压缩映射原理,提出一种自适应泛函网络循环结构和算法,通过训练该结构使其逼近于目标函数的不动点。通过算例分析表明,该算法具有计算精度高、收敛速度快等特点。所获结果对于神经计算方法的研究具有参考价值。 相似文献
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本文提出了一种新的基于泛函网络的多项式求根模型及学习算法,而泛函网络的参数利用解线性不等式组,可得到所求任意高阶多项式近似根的一般参数表达式。文章还讨论了基于泛函网络的多项式求根学习算法实现的一些技术问题,相对传统方法,能够有效地获得任意多项式对应根的参数表达式。 相似文献
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正交泛函网络函数逼近理论及算法 总被引:1,自引:1,他引:0
基于正交函数的概念和特性,提出一种正交泛函网络新模型,给出了正交泛函网络学习算法.该算法是借助于正交函数性质和Lagrange乘数法做辅助函数,对泛函参数学习过程归结为求解一组线性方程组的过程.最后,通过函数逼近算例计算机仿真结果表明,该算法十分有效,具有模型简单、逼近精度高等特点. 相似文献
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In recent years, both multilayer perceptrons and networks of spiking neurons have been used in applications ranging from detailed models of specific cortical areas to image processing. A more challenging application is to find solutions to functional equations in order to gain insights to underlying phenomena. Finding the roots of real valued monotonically increasing function mappings is the solution to a particular class of functional equation. Furthermore, spiking neural network approaches in solving problems described by functional equations, may be an useful tool to provide important insights to how different regions of the brain may co-ordinate signaling within and between modalities, thus providing a possible basis to construct a theory of brain function. In this letter, we present for the first time a spiking neural network architecture based on integrate-and-fire units and delays, that is capable of calculating the functional or iterative root of nonlinear functions, by solving a particular class of functional equation. 相似文献
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In this paper, a novel method based on feed-forward neural networks is presented for solving Fredholm integral equations of the second kind. In the present approach, we first approximate the unknown function based on neural networks, then substitute the approximate function in the appropriate error function of the integral equation, and finally train the network with as few neurons as necessary to achieve the desired accuracy. This novel method, in comparison with Harr function and Bernstein polynomials methods, shows that the use of neural networks provides solutions with very good generalizations and higher accuracy. The proposed method is illustrated by several examples. 相似文献
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Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach 总被引:8,自引:0,他引:8
The Hamilton-Jacobi-Bellman (HJB) equation corresponding to constrained control is formulated using a suitable nonquadratic functional. It is shown that the constrained optimal control law has the largest region of asymptotic stability (RAS). The value function of this HJB equation is solved for by solving for a sequence of cost functions satisfying a sequence of Lyapunov equations (LE). A neural network is used to approximate the cost function associated with each LE using the method of least-squares on a well-defined region of attraction of an initial stabilizing controller. As the order of the neural network is increased, the least-squares solution of the HJB equation converges uniformly to the exact solution of the inherently nonlinear HJB equation associated with the saturating control inputs. The result is a nearly optimal constrained state feedback controller that has been tuned a priori off-line. 相似文献
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In this paper, a numerical method which produces an approximate polynomial solution is presented for solving Lane–Emden equations as singular initial value problems. Firstly, we use an integral operator (Yousefi (2006) [4]) and convert Lane–Emden equations into integral equations. Then, we convert the acquired integral equation into a power series. Finally, transforming the power series into Padé series form, we obtain an approximate polynomial of arbitrary order for solving Lane–Emden equations. The advantages of using the proposed method are presented. Then, an efficient error estimation for the proposed method is also introduced and finally some experiments and their numerical solutions are given; and comparing between the numerical results obtained from the other methods, we show the high accuracy and efficiency of the proposed method. 相似文献
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The bounded energy optimal control for one-dimensional linear stationary distributed parameter system is solved here. The criterion function is a quadratic functional of the output. Obtaining the optimal control involves the computation of the solution of a certain non-linear integral equation. The method of solving this integral equation is approximating the kernel of the integral operator by a sequence of degenerate kernels. It is shown that the sequence of approximate solutions of the approximate integral equations converges to the optimal solution; and that the sequence of approximate values of the criterion, converges to the optimal value of the criterion. 相似文献
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Explicit approximate inverse preconditioning techniques 总被引:1,自引:0,他引:1
G. A. Gravvanis 《Archives of Computational Methods in Engineering》2002,9(4):371-402
Summary The numerical treatment and the production of related software for solving large sparse linear systems of algebraic equations,
derived mainly from the discretization of partial differential equation, by preconditioning techniques has attracted the attention
of many researchers. In this paper we give an overview of explicit approximate inverse matrix techniques for computing explicitly
various families of approximate inverses based on Choleski and LU—type approximate factorization procedures for solving sparse
linear systems, which are derived from the finite difference, finite element and the domain decomposition discretization of
elliptic and parabolic partial differential equations. Composite iterative schemes, using inner-outer schemes in conjunction
with Picard and Newton method, based on approximate inverse matrix techniques for solving non-linear boundary value problems,
are presented. Additionally, isomorphic iterative methods are introduced for the efficient solution of non-linear systems.
Explicit preconditioned conjugate gradient—type schemes in conjunction with approximate inverse matrix techniques are presented
for the efficient solution of linear and non-linear system of algebraic equations. Theoretical estimates on the rate of convergence
and computational complexity of the explicit preconditioned conjugate gradient method are also presented. Applications of
the proposed methods on characteristic linear and non-linear problems are discussed and numerical results are given. 相似文献
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A non-standard finite difference scheme is developed to solve the linear partial differential equations with time- and space-fractional derivatives. The Grunwald–Letnikov method is used to approximate the fractional derivatives. Numerical illustrations that include the linear inhomogeneous time-fractional equation, linear space-fractional telegraph equation, linear inhomogeneous fractional Burgers equation and the fractional wave equation are investigated to show the pertinent features of the technique. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is very effective and convenient for solving linear partial differential equations of fractional order. 相似文献