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arXiv · 1608.00419

A New Method for Computing $\varphi$-functions and Their Condition Numbers of Large Sparse Matrices

Gang Wu·Lu Zhang
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Abstract

We propose a new method for computing the $\varphi$-functions of large sparse matrices with low rank or fast decaying singular values. The key is to reduce the computation of $\varphi_{\ell}$-functions of a large matrix to $\varphi_{\ell+1}$-functions of some $r$-by-$r$ matrices, where $r$ is the numerical rank of the large matrix in question. Some error analysis on the new method is given. Furthermore, we propose two novel strategies for estimating 2-norm condition numbers of the $\varphi$-functions. Numerical experiments illustrate the numerical behavior of the new algorithms and show the effectiveness of our theoretical results.

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Gang Wu, Lu Zhang. 2016-08-01. A New Method for Computing $\varphi$-functions and Their Condition Numbers of Large Sparse Matrices. https://arxiv.org/abs/1608.00419

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