Two New Methods Of Solving Numerical Differentiation

Numerical differentiation is that derivative value of a function at a certain point is approximately solved in discrete method.There has been a lot of solutions to numerical differentiation.However,they have their limitations of their own.Moreover,there are relatively few researches on derivative of higher order approximation.Based on the analysis and summary of basic ideas and methods,this thesis proposes two new estimation of error of higher order approximation.Solution 1 is to research the question of higher order numerical differentiation under non-uniform distribution by using Tikhonov regularization method and constructing a five order spline funtion.Because the values of in discussion are random,this solution is of great practicability. Another solution is in addition of uniform distribution ,and based on the three-bending-moment algorithm of the cubic spline interpolation function.By making use of the bending moment weighted sum at the knots and compute the approximation of the second order derivative at the mid-point of interval.This solutions'advantages is that it is simple,easy to understand,and more higher order computational accuracy than getting two order numerical differentiation by using cubic spline interpolation function.