非负矩阵Perron根上界序列(英文)

给出了非负矩阵Perron根的一系列优化上界,即通过相似对角变换与Gerschgorin定理较好的估计了Perron根的上界,并且通过例子来说明这种方法的有效性.     

非负不可约矩阵Perron根的上界序列

给出了非负不可约矩阵Perron根的新上界序列,并指出该序列是收敛到Perron根的,最后给出两个数值例子加以说明,并与文献[1,3,6]中的结论进行了比较．     

非负矩阵Perron根的上界序列

1引言本文讨论非负矩阵Perron根的上界。设     

非负矩阵Perron根的上界

文章针对特殊的非负矩阵，应月简单的相似变换，使矩阵保持非负性且最大行和减小，从而得到行和为正非负矩阵Perron根的新上界．     

非负矩阵的Perron补与Perron根的估计

对于非负矩阵A,主要讨论其谱半径即Perron根的估计.这里提出了一种利用非负矩阵的Perron补矩阵与Perron根关系来估计其Perron根上下界的新方法,并且给出例子来说明这种方法的有效性.     

关于Liouville函函数的非线性指数和（英文）

令λ(n)是刘维尔函数.考虑β是变量的情况,并推广Sankaranarayanan和Sun的结果,用Vaughan恒等式和Perron公式证明非线性指数和的一个非平凡上界.     

非负矩阵Perron根的下界序列

非负矩阵Perron根的估计是非负矩阵理论研究的重要课题之一.如果其上下界能够表示为非负矩阵元素的易于计算的函数,那么这种估计价值更高.本文结合非负矩阵的迹分两种情况给出Perron根的下界序列,并且给出数值例子加以说明.     

计算非负不可约矩阵Perron根的对角变换

计算非负矩阵Perron根一般通过矩阵的对角变换,但是有的时候是不可行的．本文为非负不可约矩阵的计算给了一列对角变换．此种变换对所有的非负不可约矩阵实用,并且方便计算,最后给出了数值例子．     

计算非负不可约矩阵Perron根的对角变换(英文)

计算非负矩阵Perron根一般通过矩阵的对角变换,但是有的时候是不可行的.本文为非负不可约矩阵的计算给了一列对角变换.此种变换对所有的非负不可约矩阵实用,并且方便计算,最后给出了数值例子.     

非负不可约矩阵Perron根的估计

给出了非负不可约矩阵Perron根的一些上下界估计,设A为任意非负不可约矩阵,ρ(A)为其Perron根,则ρ(A)≤max{D_k,(r_1+r_2+…r_k)/k}其中D_k为矩阵A所有k阶主子阵之列和最大值,r_1≥r_2≥…≥r_n为从大到小排序的行和,所得结果易于计算且较经典的Frobienus界值精确.同时也得到一个类似下界.     

Perron's method for quasilinear hyperbolic systems: Part I

We define a notion of viscosity solution (sub-, supersolution) for these systems, prove a comparison principle and we prove existence of viscosity solutions using a Perron like method. In Part I, we do all the above except prove existence using the Perron method.     

A new differential equation method for finding the Perron root of a positive matrix

A basic problem in linear algebra is the determination of the largest eigenvalue (Perron root) of a positive matrix. In the present paper a new differential equation method for finding the Perron root is given. The method utilizes the initial value differential system developed in a companion paper for individually tracking the eigenvalue and corresponding right eigenvector of a parametrized matrix.     

Bounds for the Perron root, singularity/nonsingularity conditions, and eigenvalue inclusion sets

Using a unified approach based on the monotonicity property of the Perron root and its circuit extension, a series of exact two-sided bounds for the Perron root of a nonnegative matrix in terms of paths in the associated directed graph is obtained. A method for deriving the so-called mixed upper bounds is suggested. Based on the upper bounds for the Perron root, new diagonal dominance type conditions for matrices are introduced. The singularity/nonsingularity problem for matrices satisfying such conditions is analyzed, and the associated eigenvalue inclusion sets are presented. In particular, a bridge connecting Gerschgorin disks with Brualdi eigenvalue inclusion sets is found. Extensions to matrices partitioned into blocks are proposed.     

A modified algorithm for the Perron root of a nonnegative matrix

An algorithm of diagonal transformation for the Perron root of nonnegative matrices is proposed by Duan and Zhang [F. Duan, K. Zhang, An algorithm of diagonal transformation for Perron root of nonnegative irreducible matrices, Appl. Math. Comput. 175 (2006) 762-772]. This method can be used for all nonnegative irreducible matrices. In this paper, an improved algorithm which is based on this method is proposed. The new algorithm inherits all the above-mentioned advantages of the original algorithm and has higher efficiency. It is testified by numerical testing that the efficiency of the new algorithm is improved greatly.     

Existence of multi-valued solutions with asymptotic behavior of Hessian equations

In this paper, we use the Perron method to prove the existence of multi-valued solutions with asymptotic behavior at infinity of Hessian equations.     

A new version of a theorem of Minh–Räbiger–Schnaubelt regarding nonautonomous evolution equations

We develop a new version of a known theorem obtained by Van Minh, Räbiger, Schnaubelt in [N. Van Minh, F. Räbiger and R. Schnaubelt, Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half line, Integral Equ. Oper. Theory 32 (1998) pp. 332–353]. We rely completely on the classical ‘test functions’ method designed by Perron in 1930. The advantage of such a version is that is more readable since the classical method of Perron have been known for decades and that we do not involve a sophisticated mathematical machinery. Our approach is in contrast with the general philosophy of ‘autonomization’ the nonautonomous system, since we do not require to attach the evolution semigroup. Also we point out a discrete-time version of our approach extending some known results given by Li and Henry.     

完全非线性一致椭圆方程的外问题

利用Perron方法得到了完全非线性一致椭圆方程外问题具有渐近性质的粘性解的存在性.     

A set oriented definition of finite-time Lyapunov exponents and coherent sets

The problem of phase space transport, which is of interest from both the theoretical and practical point of view, has been investigated extensively using geometric and probabilistic methods. Two important tools to study this problem that have emerged in recent years are finite-time Lyapunov exponents (FTLE) and the Perron–Frobenius operator. The FTLE measures the averaged local stretching around reference trajectories. Regions with high stretching are used to identify phase space transport barriers. One probabilistic method is to consider the spectrum of the Perron–Frobenius operator of the flow to identify almost-invariant densities. These almost-invariant densities are used to identify almost invariant sets. In this paper, a set-oriented definition of the FTLE is proposed which is applicable to phase space sets of finite size and reduces to the usual definition of FTLE in the limit of infinitesimal phase space elements. This definition offers a straightforward connection between the evolution of probability densities and finite-time stretching experienced by phase space curves. This definition also addresses some concerns with the standard computation of the FTLE. For the case of autonomous and periodic vector fields we provide a simplified method to calculate the set-oriented FTLE using the Perron–Frobenius operator. Based on the new definition of the FTLE we propose a simple definition of finite-time coherent sets applicable to vector fields of general time-dependence, which are the analogues of almost-invariant sets in autonomous and time-periodic vector fields. The coherent sets we identify will necessarily be separated from one another by ridges of high FTLE, providing a link between the framework of coherent sets and that of codimension one Lagrangian coherent structures. Our identification of coherent sets is applied to three examples.