Results 21 to 30 of about 26,944 (191)
On large-scale diagonalization techniques for the Anderson model of localization [PDF]
, 2006 We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for large-scale sparse real and symmetric indefinite matrices of ...
Bollhofer, Matthias +8 more
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On the Neumann eigenvalues for second-order Sturm–Liouville difference equations
Advances in Difference Equations, 2020 The paper is concerned with the Neumann eigenvalues for second-order Sturm–Liouville difference equations. By analyzing the new discriminant function, we show the interlacing properties between the periodic, antiperiodic, and Neumann eigenvalues ...
Yan-Hsiou Cheng
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Minimum number of distinct eigenvalues of graphs [PDF]
The Electronic Journal of Linear Algebra, 2013 The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph $G$, is denoted by $q(G)$. Using other parameters related to $G$, bounds for $q(G)$ are proven and then applied to deduce further properties of $q(G)$. It is shown that there is a great number of graphs $G$ for which $q(G)=2$.
Ahmadi, Bahman +5 more
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Estimates for the minimum eigenvalue of an M-matrix
Journal of Physics: Conference Series, 2023 Abstract New sharper lower bounds for the minimal eigenvalues of symmetric M-matrices and nonsymmetric M-matrices are proposed by constructing two increasing sequences. By contrasting the proposed instances with the related findings, two instances are offered to demonstrate the effectiveness of the technique.
Qin Zhong, Ling Li
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On the second minimizing graph in the set of complements of trees
AKCE International Journal of Graphs and Combinatorics, 2019 Let G be a graph of order n and A(G)=[ai,j]be its adjacency matrix such that ai,j=1 if viis adjacent to vjand ai,j=0 otherwise, where 1≤i,j≤n. In a certain family of graphs, a graph is called minimizing (or second minimizing) if the least eigenvalue of ...
M. Javaid
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On the minimum number of distinct eigenvalues of a threshold graph [PDF]
Linear Algebra and its Applications, 2022 For a graph $G$, we associate a family of real symmetric matrices, $S(G)$, where for any $A\in S(G)$, the location of the nonzero off-diagonal entries of $A$ are governed by the adjacency structure of $G$. Let $q(G)$ be the minimum number of distinct eigenvalues over all matrices in $S(G)$.
Shaun Fallat, Seyed Ahmad Mojallal
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HUBO formulations for solving the eigenvalue problem
Results in Control and Optimization, 2023 Solving the eigenvalue problem is particularly important in almost all fields of science and engineering. With the development of quantum computers, multiple algorithms have been proposed for this purpose.
Kyungtaek Jun, Hyunju Lee
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On completely regular codes with minimum eigenvalue in geometric graphs
Discrete Mathematics, 2023 We prove that any completely regular code with minimum eigenvalue in any geometric graph G corresponds to a completely regular code in the clique graph of G. Studying the interrelation of these codes, a complete characterization of the completely regular codes in the Johnson graphs J(n,w) with covering radius w-1 and strength 1 is obtained.
Ivan Yu. Mogilnykh +1 more
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Minimum Supports of Eigenfunctions with the Second Largest Eigenvalue of the Star Graph [PDF]
The Electronic Journal of Combinatorics, 2020 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 $n-2$.
Vladislav V. Kabanov +3 more
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Bounds on the Minimum Edge Dominating Energy in Terms of Some Parameters of a Graph [PDF]
Mathematics Interdisciplinary Research, 2023 The minimum edge dominating energy, denoted by $EE_{F}(G)$, is the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of graph $G$.
Fateme Movahedi
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