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Least-Squares Spectral Methods for ODE Eigenvalue Problems
SIAM Journal on Scientific Computing, 2022 We develop spectral methods for ODEs and operator eigenvalue problems that are based on a least-squares formulation of the problem. The key tool is a method for rectangular generalized eigenvalue problems, which we extend to quasimatrices and objects combining quasimatrices and matrices.
Behnam Hashemi, Yuji Nakatsukasa
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The domination number and the least $Q$-eigenvalue [PDF]
Applied Mathematics and Computation, 2013 A vertex set $D$ of a graph $G$ is said to be a dominating set if every vertex of $V(G)\setminus D$ is adjacent to at least a vertex in $D$, and the domination number $\gamma(G)$ ($\gamma$, for short) is the minimum cardinality of all dominating sets of $
Guo, Shu-Guang +3 more
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Resonant semilinear Robin problems with a general potential [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2017 We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. The reaction term is a Carath\'eodory function which is resonant with respect to any nonprincipal eigenvalue both at $\pm \infty$ and 0.
Nikolaos Papageorgiou +2 more
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The least eigenvalue of signless Laplacian of non-bipartite graphs with given domination number
Discrete Mathematics, 2014 Let $G$ be a connected non-bipartite graph on $n$ vertices with domination number $\gamma \le \frac{n+1}{3}$. We investigate the least eigenvalue of the signless Laplacian of $G$, and present a lower bound for such eigenvalue in terms of the domination ...
Fan, Yi-Zheng, Tan, Ying-Ying
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The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic
Discussiones Mathematicae Graph Theory, 2015 A graph in a certain graph class is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum among all graphs in that class. Bell et al.
Wang Yi +3 more
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Graphs for which the least eigenvalue is minimal, II
Linear Algebra and its Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bell, Francis K +3 more
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On distance-regular graphs with smallest eigenvalue at least −m
Journal of Combinatorial Theory, Series B, 2010 A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer $m\geq 2$, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least $-m$, diameter at least three and intersection ...
Koolen, JH, Bang, S
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Universal Completability, Least Eigenvalue Frameworks, and Vector Colorings. [PDF]
Discrete Comput Geom, 2017 25 ...
Godsil C +4 more
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Controllable graphs with least eigenvalue at least -2 [PDF]
Applicable Analysis and Discrete Mathematics, 2011 Connected graphs whose eigenvalues are distinct and main are called controllable graphs in view of certain applications in control theory. We give some general characterizations of the controllable graphs whose least eigenvalue is bounded from below by - 2; in particular, we determine all the controllable exceptional graphs.
Dragos Cvetkovic +3 more
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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 be a graph of order and be its adjacency matrix such that if is adjacent to and otherwise, where . In a certain family of graphs, a graph is called minimizing (or second minimizing) if the least eigenvalue of its adjacency matrix attains the minimum (
M. Javaid
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