A New Method for Computing φ-functions and Their Condition Numbers of Large Sparse Matrices

2016/08/01 by Wu, Gang, Zhang, Lu
#65F15 #65F35 #65F60 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1608.00419

Abstract

We propose a new method for computing the φ-functions of large sparse matrices with low rank or fast decaying singular values. The key is to reduce the computation of φ_ℓ-functions of a large matrix to φ_ℓ+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 φ-functions. Numerical experiments illustrate the numerical behavior of the new algorithms and show the effectiveness of our theoretical results.

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