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arxiv:2011.04366
Derivatives of partial eigendecomposition of a real symmetric matrix for degenerate cases
Published on Nov 9, 2020
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Abstract
The paper derives forward and backward derivatives for partial eigendecomposition of real symmetric matrices under degeneracy, enabling stable computation without resolving repeated eigenvalues.
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This paper presents the forward and backward derivatives of partial eigendecomposition, i.e. where it only obtains some of the eigenpairs, of a real symmetric matrix for degenerate cases. The numerical calculation of forward and backward derivatives can be implemented even if the degeneracy never disappears and only some eigenpairs are available.
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