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SIAMSC

2011

2011

Given a certain function f, various methods have been proposed in the past for addressing the important problem of computing the matrix-vector product f(A)b without explicitly computing the matrix f(A). Such methods were typically developed for a speciﬁc function f, a common case being that of the exponential. This paper discusses a procedure based on least squares polynomials that can, in principle, be applied to any (continuous) function f. The idea is to start by approximating the function by a spline of a desired accuracy. Then, a particular deﬁnition of the function inner product is invoked that facilitates the computation of the least squares polynomial to this spline function. Since the function is approximated by a polynomial, the matrix A is referenced only through a matrix-vector multiplication. In addition, the choice of the inner product makes it possible to avoid numerical integration. As an important application, we consider the case when f(t) = √ t and A is a spars...

Related Content

Added |
15 May 2011 |

Updated |
15 May 2011 |

Type |
Journal |

Year |
2011 |

Where |
SIAMSC |

Authors |
Jie Chen, Mihai Anitescu, Yousef Saad |

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