Results 1 to 10 of about 242,274 (310)
Maximum and Minimum First Eigenvalues for a Class of Elliptic Operators [PDF]
Proceedings of the American Mathematical Society, 1966 By the maximum principle all the X's are positive (see [l]). Bounds for the X's were established under various hypotheses by Duffin [2], Protter-Weinberg [3]. Here we want to determine if A has a maximum or a minimum and for what operator in £„ the maximum or minimum occurs. Let Ma, ma denote the maximizing and minimizing operator relative to the class
Carlo Pucci
+5 more sources
Bicyclic graphs for which the least eigenvalue is minimum
Linear Algebra and its Applications, 2008 AbstractThe spread of a graph is defined to be the difference between the greatest eigenvalue and the least eigenvalue of the adjacency matrix of the graph. In this paper we determine the unique graph with minimum least eigenvalue among all connected bicyclic graphs of order n.
Miroslav Petrović +2 more
openalex +3 more sources
Several new inequalities for the minimum eigenvalue of M-matrices [PDF]
Journal of Inequalities and Applications, 2016 Several convergent sequences of the lower bounds for the minimum eigenvalue of M-matrices are given. It is proved that these sequences are monotone increasing and improve some existing results.
Jianxing Zhao, Caili Sang
doaj +3 more sources
New bounds for the minimum eigenvalue of 𝓜-tensors
Open Mathematics, 2017 A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal.
Zhao Jianxing, Sang Caili
doaj +3 more sources
Minimum eigenvalues for positive, Rockland operators [PDF]
Proceedings of the American Mathematical Society, 1985 Let L L be a positive, Rockland operator of homogeneous degree γ \gamma . The minimum eigenvalue of d π ( L ) d\pi (L) increases as the γ \gamma th power of the homogeneous distance from the origin of the orbit corresponding to π \pi
Andrzej Hulanicki +2 more
openalex +2 more sources
New bounds for the minimum eigenvalue of M-matrices
Open Mathematics, 2016 Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices.
Wang Feng, Sun Deshu
doaj +3 more sources
Symmetric schemes for computing the minimum eigenvalue of a symmetric Toeplitz matrix [PDF]
Linear Algebra and its Applications, 1999 In [8] and [9] W. Mackens and the present author presented two generalizations of a method of Cybenko and Van Loan [4] for computing the smallest eigenvalue of a symmetric, positive definite Toeplitz matrix. Taking advantage of the symmetry or skew-symmetry of the corresponding eigenvector both methods are improved considerably.
Heinrich Voß
openalex +3 more sources
A Nordhaus–Gaddum conjecture for the minimum number of distinct eigenvalues of a graph [PDF]
Linear Algebra and its Applications, 2018 We propose a Nordhaus-Gaddum conjecture for $q(G)$, the minimum number of distinct eigenvalues of a symmetric matrix corresponding to a graph $G$: for every graph $G$ excluding four exceptions, we conjecture that $q(G)+q(G^c)\le |G|+2$, where $G^c$ is the complement of $G$.
Rupert H. Levene +2 more
openalex +4 more sources
Graph diameter, eigenvalues, and minimum-time consensus [PDF]
Automatica, 2013 We consider the problem of achieving average consensus in the minimum number of linear iterations on a fixed, undirected graph. We are motivated by the task of deriving lower bounds for consensus protocols and by the so-called "definitive consensus conjecture" which states that for an undirected connected graph G with diameter D there exist D matrices ...
Julien M. Hendrickx +3 more
openalex +5 more sources
Minimum supports of eigenfunctions with the second largest eigenvalue of the Star graph [PDF]
The Electronic Journal of Combinatorics, 2019 The Star graph $S_n$, $n\ge 3$, is the Cayley graph on the symmetric group $Sym_n$ generated by the set of transpositions $\{(12),(13),\ldots,(1n)\}$. In this work we study eigenfunctions of $S_n$ corresponding to the second largest eigenvalue $n-2$.
V. V. Kabanov +3 more
openalex +5 more sources