Function approximation using gradient information with application to parametric and stochastic differential equations
For researchers in scientific computing and differential equations, this offers a more efficient approximation method, though the improvement is incremental.
The paper enhances multivariate function approximation by incorporating derivative information into the least squares method, reducing function evaluations while maintaining accuracy. Numerical examples demonstrate improved efficiency over standard LSM.
In the paper we consider the problem of multivariate function approximation in polynomial basis. In order to solve this problem, we adjust the least squares method (LSM) by adding information about derivatives of the function. This modification allows reducing the number of evaluations of approximating function while keeping the accuracy at the appropriate level. We propose several techniques for time-efficient calculation of derivatives in various applications. Numerical examples are given for comparison between the standard LSM and the proposed approach.