A variational method for numerical differentiation
Numerische Mathematik
Journal of Computational and Applied Mathematics
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
New finite difference formulas for numerical differentiation
Journal of Computational and Applied Mathematics
Numerical Methods for Scientists and Engineers
Numerical Methods for Scientists and Engineers
Scientific Computing: An Introductory Survey
Scientific Computing: An Introductory Survey
Numerical Methods Using MATLAB
Numerical Methods Using MATLAB
Automatic differentiation of algorithms: from simulation to optimization
Automatic differentiation of algorithms: from simulation to optimization
Numerical Methods
Journal of Computational and Applied Mathematics
Taylor series based finite difference approximations of higher-degree derivatives
Journal of Computational and Applied Mathematics
Simplified analytical expressions for numerical differentiation via cycle index
Journal of Computational and Applied Mathematics
A remainder formula of numerical differentiation for the generalized Lagrange interpolation
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Summation-by-parts operators and high-order quadrature
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 7.30 |
Through introducing the generalized Vandermonde determinant, the linear algebraic system of a kind of Vandermonde equations is solved analytically by use of the basic properties of this determinant, and then we present general explicit finite difference formulas with arbitrary order accuracy for approximating first and higher derivatives, which are applicable to unequally or equally spaced data. Comparing with other finite difference formulas, the new explicit difference formulas have some important advantages. Basic computer algorithms for the new formulas are given, and numerical results show that the new explicit difference formulas are quite effective for estimating first and higher derivatives of equally and unequally spaced data.