These methods require the ability to repeatedly perform operations on the Hessian such as multiplication with arbitrary vectors, solving linear systems, ...
Mar 23, 2020 · In this work, we describe algorithms for constructing and updating hierarchical matrix approximations of Hessians, and illustrate them on a number of ...
Sep 11, 2024 · Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient ...
Mar 23, 2020 · The Hessian operator plays a central role in optimization of systems governed by partial differential equations (PDEs), also known as PDE-.
For inverse problems governed by partial differential equations (PDEs) with high-rank Hessians, the resulting number of forward/adjoint PDE solves may be ...
Jan 1, 2020 · "Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs". SIAM Journal on Scientific Computing 42 (5).
Jan 9, 2023 · In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format.
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In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In ...
Jun 26, 2023 · In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix ...
In this dissertation, we describe algorithmic approaches for the Newton-based solution of large-scale computational inverse problems governed by PDEs.