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Smoothness of Hessenberg and Bidiagonal Forms - Administration - people math gatech

Smoothness of Hessenberg and Bidiagonal Forms - Administration - people math gatech 2025

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The document discusses the smoothness properties of transformations of matrix-valued functions to Hessenberg and bidiagonal forms. It explores the relationship between these transformations and the rank of associated Krylov functions, providing sufficient conditions for the existence of smooth decompositions. The authors present theoretical results on the differentiability of these forms, emphasizing their relevance for efficient algorithms in numerical linear algebra, particularly in computing eigenvalues and singular value decompositions.

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