Abstract:We consider the numerical evaluation of the quantity $Af(A^{-1}B)$, where $A$ is Hermitian positive definite, $B$ is Hermitian, and $f$ is a function defined on the spectrum of $A^{-1}B$. This problem is related to the Hermitian-definite matrix pencil $B-\lambda A$. We study the conditioning of the problem, and we introduce several algorithms that combine the Schur decomposition with either the matrix square root or the Cholesky factorization. We study the numerical behavior of these algorithms in floating-point arithmetic, assess their computational costs, and compare their numerical performance. Our analysis suggests that the algorithms based on the Cholesky factorization will be more accurate and efficient than those based on the matrix square root. This is confirmed by our numerical experiments.
| Subjects: | Numerical Analysis (math.NA) |
| Cite as: | arXiv:2510.16473 [math.NA] |
| (or arXiv:2510.16473v2 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2510.16473 arXiv-issued DOI via DataCite |
From: Massimiliano Fasi [view email]
[v1]
Sat, 18 Oct 2025 12:41:11 UTC (35 KB)
[v2]
Fri, 22 May 2026 12:56:26 UTC (57 KB)
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