Function approximation using gradient information with application to\n parametric and stochastic differential equations

2018/02/05 by Gleb Ryzhakov, Ivan Oseledets, Ryzhakov, Gleb +1
Mathematics · #35C11 #41A10 #65D05 #65D15 #FOS: Mathematics #Numerical Analysis (math.NA) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1802.01542

openalex publication_date 2018/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper we consider the problem of multivariate function approximation\nin polynomial basis. In order to solve this problem, we adjust the least\nsquares method (LSM) by adding information about derivatives of the function.\nThis modification allows reducing the number of evaluations of approximating\nfunction while keeping the accuracy at the appropriate level. We propose\nseveral techniques for time-efficient calculation of derivatives in various\napplications. Numerical examples are given for comparison between the standard\nLSM and the proposed approach.\n

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