线性算子的不变多面体及其在小波和细分正则性的应用
Invariant polytopes of linear operators with applications to regularity of wavelets and of subdivisions
AI总结：
本文推广了计算联合谱半径的不变多面体算法，并将其扩展到更广泛的矩阵集，用于解决小波和细分的正则性问题。
摘要：
我们推广了最近用于计算联合谱半径的不变多面体算法，并将其扩展到更广泛的矩阵集。这使得该算法可以应用于具有有限多个谱最大化乘积的矩阵集。证明了该算法的收敛性准则。作为应用，我们解决了两个具有挑战性的计算开放问题。首先，我们确定了不同参数ω下的Butterfly细分方案的正则性。在
英文摘要：
We generalize the recent invariant polytope algorithm for computing the joint spectral radius and extend it to a wider class of matrix sets. This, in particular, makes the algorithm applicable to sets of matrices that have finitely many spectrum maximizing products. A criterion of convergence of the algorithm is proved. As an application we solve two challenging computational open problems. First we find the regularity of the Butterfly subdivision scheme for various parameters $ω$. In the "most regular" case $ω= \frac{1}{16}$, we prove that the limit function has Hölder exponent $2$ and its derivative is "almost Lipschitz" with logarithmic factor $2$. Second we compute the Hölder exponent of Daubechies wavelets of high order.
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