Approximating the diagonal of a Hessian: which sample set of points\n should be used

2021/04/23 by Gabriel Jarry–Bolduc, Jarry-Bolduc, Gabriel
Earth and Planetary Sciences · Engineering · Medicine · Physics and Astronomy · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Hydrocarbon exploration and reservoir analysis #Medical Imaging Techniques and Applications #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.2104.11821

openalex publication_date 2021/04/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

An explicit formula to approximate the diagonal entries of the Hessian is\nintroduced. When the derivative-free technique called \generalized\ncentered simplex gradient is used to approximate the gradient, then the\nformula can be computed for only one additional function evaluation. An error\nbound is introduced and provides information on the form of the sample set of\npoints that should be used to approximate the diagonal of a Hessian. If the\nsample set of points is built in a specific manner, it is shown that the\ntechnique is \O(\Δ_S²) accurate approximation of the diagonal\nentries of the Hessian where \Δ_S is the radius of the sample set.\n

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