Abstract: Compared with the traditional multi-layer perceptron model, Chebyshev neural network has fast convergence, low complexity and generalization ability advantages. However, the one variable Chebyshev neural network to solve multivariate problems in the practical application is great limitations. For this problem, the paper extends and proposes multivariate Chebyshev neural network model and gives fast weight determination algorithm which base on Chebyshev polynomials orthogonal. The simulation results show that compared to traditional multi-layer perceptron neural network, the method has obvious advantages in the calculation accuracy and computing speed.

Key words: neural networks, Chebyshev polynomial, multivariate function, quick calculation of the weights

摘要： 与传统的多层感知器模型相比，切比雪夫神经网络具有收敛速度快，复杂度低，泛化能力强等优点，但是，其研究最为广泛的一元切比雪夫神经网络在解决实际应用中的多元问题时存在着很大局限。鉴于此，对一元切比雪夫神经网络进行扩展，提出了多元切比雪夫神经网络模型，并在切比雪夫多项式正交性的基础上给出了快速权值确定算法。仿真实验证明，相对于传统多层感知器神经网络，该方法在计算精度和计算速度等方面都存在明显优势。

关键词: 神经网络, 切比雪夫多项式, 多元函数, 权值快速计算