Recently, Uhlig [Numer. Algorithms, 52(3):335-353, 2009] proposed open questions about the ratios between the spectral norm, the numerical radius and the spectral radius of a square matrix. In this note, we provide some observations to answer these questions. Keywords—Spectral norm, Numerical radius, Spectral radius, Ratios

This is a sequel to an accepted talk of WAW 2011, where we introduced a set of generalized Laplacians of hypergraphs through the high-ordered random walks. In that paper, we proved the eigenvalues of these Laplacians can effectively control the mixing rate of highordered random walks, the generalized distances/diameters, and the edge expansions. In this talk, we will give a preliminary report o...

We study the mean size of wavelet packets in Lp. An exact formula for the mean size is given in terms of the p-norm joint spectral radius. This will be a corollary of an asymptotic formula for the Lp-norms on the subdivision trees. Then the stability and Schauder basis property of wavelet packets in Lp, and the instability of biorthogonal wavelet packets in L2 are analyzed. AMS Subject Classifi...

The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of...

In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the ex...

Abstract. The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The precision of the asymptotic depends on the joint spectral radius of the linear representation of...

Abstract We prove new mixing rate estimates for the random walks on homogeneous spaces determined by a probability distribution finite group $G$ . introduce switched walk set of distributions , that its long-term behaviour is Fourier joint spectral radius distributions, and give Hermitian sum-of-squares algorithms effective estimation this quantity.

Fluid flow in jointed rock mass with impermeable matrix is often controlled by joint properties, including aperture, orientation, spacing, persistence and etc. On the other hand, since the rock mass is made of heterogeneous and anisotropic natural materials, geometric properties of joints may have dispersed values. One of the most powerful methods for simulation of stochastic nature of geometri...