Faber polynomials of matrices for non-convex sets
Faber polynomials of matrices for non-convex sets
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非凸集矩阵的 Faber 多项式
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Crouzeix
中科院分区：
文献类型：
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作者：
B. Beckermann;M. Crouzeix
最近证明了$|| F_n(A) ||leq 2$，其中$A$是作用于Hilbert空间的线性连续算子，$F_n$是阶$n$的Faber多项式，对应于包含$A$数值范围的某个凸紧集$Esubset mathbb C$。这样的不等式在数值线性代数中是有用的，它允许例如推导出Krylov子空间方法的误差界。本文将此结果推广到非必要凸集$E$。
It has been recently shown that $|| F_n(A) ||leq 2$, where $A$ is a linear continuous operator acting in a Hilbert space, and $F_n$ is the Faber polynomial of degree $n$ corresponding to some convex compact $Esubset mathbb C$ containing the numerical range of $A$. Such an inequality is useful in numerical linear algebra, it allows for instance to derive error bounds for Krylov subspace methods. In the present paper we extend this result to not necessary convex sets $E$.