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arXiv · 2603.10514

Estimating the condition number of Chebyshev filtered vectors with application to the ChASE library

Edoardo Di Napoli·Xinzhe Wu
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Abstract

Chebyshev filtered subspace iteration is a well-known algorithm for the solution of (symmetric/Hermitian) algebraic eigenproblems which has been implemented in several application codes~\cite{Kronik:2006ff, abinit:2020} or in stand alone libraries~\cite{ChASE}. An essential part of the algorithm is the QR-factorization of the array of vectors spanning the active subspace that have been filtered by the Chebyshev filter. Typically such an array has an a-priori unknown high condition number that directly influences the choice of QR-factorization algorithm. In this work we show how such condition number can be bound from above with precise and inexpensive estimates. We then proceed to use these estimates to implement a mechanism for the choice of QR-factorization in the ChASE library. We show how such mechanism enhance the performance of the library without compromising on its accuracy.

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Edoardo Di Napoli, Xinzhe Wu. 2026-03-11. Estimating the condition number of Chebyshev filtered vectors with application to the ChASE library. https://arxiv.org/abs/2603.10514

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