Derivatives of partial eigendecomposition of a real symmetric matrix for\n degenerate cases

2020/11/09 by Muhammad Kasim, Kasim, Muhammad Firmansyah
Computer Science · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.2011.04366

openalex publication_date 2020/11/09 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

This paper presents the forward and backward derivatives of partial\neigendecomposition, i.e. where it only obtains some of the eigenpairs, of a\nreal symmetric matrix for degenerate cases. The numerical calculation of\nforward and backward derivatives can be implemented even if the degeneracy\nnever disappears and only some eigenpairs are available.\n

Citations

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• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
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