摘要
将神经网络用于线性系统方程的求解问题 ,但所用的准则函数不是通常的最小二乘函数 ,而是l∞(或Chebyshev)范数准则函数 ,即E∞(x) =maxx∈Rn{ |ri(x) |}或E∞(x) =maxx∈Rn12 r2i(x) .先将E∞(x)光滑化 ,再利用神经网络来求解无约束光滑优化问题。并讨论了网络的收敛性和稳定性。
In the paper,neural networks are applied to explore the solving problem of linear equations.The critria is l ∞ —norm(or Chebyshev' snorm),i.e. E ∞(x)= max x∈R n｛｜r i(x)｜｝或E ∞(x)= max x∈R n12r 2 i(x) instead of usual last-squares criteria.We first smooth the objective function E ∞(x) .Then we explore the unconstrained optimization problem by using neural networks.The convergence and stability of the network are discussed. [WT5HZ]
出处
《重庆大学学报（自然科学版）》
CAS
CSCD
2000年第2期102-104,119,共4页
Journal of Chongqing University
