一种基于切比雪夫插值的联想记忆系统

提出了一种基于切比雪夫插值的高阶联想记忆系统(TI-AMS),能提供对任意阶多变量多项式函数的无误差逼近.切比雪夫插值的近似于最优一致逼近的性质从理论上保证了对任意连续函数的全局逼近精度.特别在对一些不连续函数(如矩形脉冲函数)的逼近中也有其它AMS无法比拟的优势.理论分析和数值模拟表明,该系统具有计算简单、学习精度高、收敛速度快、总的存储单元空间较小等优点.可广泛应用于图像压缩、模式识别、及高精度实时智能控制等领域.

A New Associative Memory System via Tchebycheff Interpolation

A new high order associative memory system via Tchebycheff interpolation is proposed. It offers the error free approximation to multi variable polynomial functions with arbitrarily given order. Tchebycheff interpolation nears to the best uniform approximation, this ensures theoretically the approximation precision as a whole to multi variable continuous functions with arbitrarily given order. Particularly, comparing with other AMS, it also has distinctive advantage in approximation to some discontinuous functions such as rectangular pulse function. Theoretic analysis and numerical simulations have shown that the proposed TI AMS has the advantages in much less computational, high precision of learning, fast convergence rate and much less required whole memory size. It has great potential in the application areas of picture compression, pattern recognition, and controller implementation for high precision real time intelligent control.