### Abstract

Given a large square matrix $A$ and a sufficiently regular function $f$ so that $f(A)$ is well defined, we are interested in the approximation of the leading singular values and corresponding singular vectors of $f(A)$, and in particular of $\|f(A)\|$, where $\|\cdot \|$ is the matrix norm induced by the Euclidean vector norm. Since neither $f(A)$ nor $f(A)v$ can be computed exactly, we introduce and analyze an inexact Golub-Kahan-Lanczos bidiagonalization procedure, where the inexactness is related to the inaccuracy of the operations $f(A)v$, $f(A)^*v$. Particular outer and inner stopping criteria are devised so as to cope with the lack of a true residual. Numerical experiments with the new algorithm on typical application problems are reported.

Original language | English |
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Publisher | s.n. |

Number of pages | 22 |

Publication status | Published - 2015 |

### Publication series

Name | arXiv |
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Volume | 1505.03453 [math.NA] |

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## Cite this

Gaaf, S. W., & Simoncini, V. (2015).

*Approximating the leading singular triplets of a large matrix function*. (arXiv; Vol. 1505.03453 [math.NA]). s.n.