The Lagrange Polynomial Interpolation is applied to polynomially characterize an unknown function passing through several points,or to approximate a known non-polynomial function with polyno-mial functions,widely used in many fields. In this paper,a derivation extension of Lagrange Polynomi-al Interpolation capable of approximating the target function with the values as well as the variation tend-ency of the interpolations is presented. Knowing each derivation within the given order at the interpola-tion points,target function could be polynomially approximated more deeply using the derivation exten-sion of Lagrange Polynomial Interpolation. Experiment results show that the cipher-text neural network constructed by the derivation extension of Lagrange Polynomial Interpolation instead of the logistic func-tion has higher training accuracy and smaller mean square error,indicating that derivation extension of Lagrange Polynomial Interpolation could be applied to more general scenarios.
关键词
拉格朗日插值公式导数推广/密文训练神经网络/多项式逼近/激励函数
Key words
Derivation extension of Lagrange Polynomial Interpolation/Cipher-text Training Neural Network/polynomial approximation/activation function
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