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• W4385377123 abstract "Abstract This work presents a novel matrix-based method for constructing an approximation Hessian using only function evaluations. The method requires less computational power than interpolation-based methods and is easy to implement in matrix-based programming languages such as MATLAB. As only function evaluations are required, the method is suitable for use in derivative-free algorithms. For reasonably structured sample sets, the method is proven to create an order-$1$ accurate approximation of the full Hessian. Under more specialized structures, the method is proved to yield order-$2$ accuracy. The underdetermined case, where the number of sample points is fewer than required for full interpolation, is studied and error bounds are developed for the resulting partial Hessians." @default.
• W4385377123 created "2023-07-30" @default.
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• W4385377123 date "2023-07-28" @default.
• W4385377123 modified "2023-09-27" @default.
• W4385377123 title "A matrix algebra approach to approximate Hessians" @default.
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• W4385377123 doi "https://doi.org/10.1093/imanum/drad056" @default.
• W4385377123 hasPublicationYear "2023" @default.
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