Characterizing the positive semidefiniteness of signed Laplacians via Effective Resistances

2016 ◽  
Author(s):  
Wei Chen ◽  
Ji Liu ◽  
Yongxin Chen ◽  
Sei Zhen Khong ◽  
Dan Wang ◽  
...  
Keyword(s):  
Positive Semidefiniteness

scholarly journals An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative Matrices

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Gang Wang ◽  
Lihong Sun
Keyword(s):  
Efficient Algorithm ◽  
Positive Definiteness ◽  
Numerical Results ◽  
Nonnegative Matrices ◽  
Maximal Eigenvalue ◽  
Positive Semidefiniteness ◽  
Maximal Eigenvalues ◽  
Modified Algorithm

In this paper, we propose an improved power algorithm for finding maximal eigenvalues. Without any partition, we can get the maximal eigenvalue and show that the modified power algorithm is convergent for zero symmetric reducible nonnegative matrices. Numerical results are reported to demonstrate the effectiveness of the modified power algorithm. Finally, a modified algorithm is proposed to test the positive definiteness (positive semidefiniteness) of Z-matrices.

scholarly journals On (conditional) positive semidefiniteness in a matrix-valued context

2017 ◽  
Vol 236 (2) ◽  
pp. 143-192 ◽  
Author(s):  
Fritz Gesztesy ◽  
Michael Pang
Keyword(s):  
Positive Semidefiniteness

scholarly journals Indefinite Kernel Network withlq-Norm Regularization

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Zhongfeng Qu ◽  
Hongwei Sun
Keyword(s):  
Probability Measure ◽  
Kernel Function ◽  
Error Bounds ◽  
Kernel Learning ◽  
Cone Condition ◽  
Input Space ◽  
Indefinite Kernel ◽  
Positive Semidefiniteness ◽  
Step Stone ◽  
Learning Rates

We study the asymptotical properties of indefinite kernel network withlq-norm regularization. The framework under investigation is different from classical kernel learning. Positive semidefiniteness is not required by the kernel function. By a new step stone technique, without any interior cone condition for input spaceXandLτcondition for the probability measureρX, satisfied error bounds and learning rates are deduced.

scholarly journals A note on the positive semidefiniteness of A(G)

2017 ◽  
Vol 519 ◽  
pp. 156-163 ◽  
Author(s):  
Vladimir Nikiforov ◽  
Oscar Rojo
Keyword(s):  
Positive Semidefiniteness

scholarly journals Krein Parameters of Fiber-Commutative Coherent Configurations

2020 ◽  
Vol 27 (01) ◽  
pp. 1-10
Author(s):  
Keiji Ito ◽  
Akihiro Munemasa
Keyword(s):  
Generalized Quadrangle ◽  
Coherent Configuration ◽  
Positive Semidefiniteness ◽  
The Absolute ◽  
Krein Condition ◽  
Coherent Configurations

For fiber-commutative coherent configurations, we show that Krein parameters can be defined essentially uniquely. As a consequence, the general Krein condition reduces to positive semidefiniteness of finitely many matrices determined by the parameters of a coherent configuration. We mention its implications in the coherent configuration defined by a generalized quadrangle. We also simplify the absolute bound using the matrices of Krein parameters.

scholarly journals POSITIVE SEMIDEFINITENESS OF DISCRETE QUADRATIC FUNCTIONALS

2003 ◽  
Vol 46 (3) ◽  
pp. 627-636 ◽  
Author(s):  
Martin Bohner ◽  
Ondřej Došlý ◽  
Werner Kratz
Keyword(s):  
Sufficient Conditions ◽  
Positive Definiteness ◽  
Quadratic Functional ◽  
Quadratic Functionals ◽  
Positive Semidefiniteness ◽  
Difference Systems ◽  
Special Cases ◽  
Even Order ◽  
Sturm Liouville ◽  
Necessary And Sufficient

AbstractWe consider symplectic difference systems, which contain as special cases linear Hamiltonian difference systems and Sturm–Liouville difference equations of any even order. An associated discrete quadratic functional is important in discrete variational analysis, and while its positive definiteness has been characterized and is well understood, a characterization of its positive semidefiniteness remained an open problem. In this paper we present the solution to this problem and offer necessary and sufficient conditions for such discrete quadratic functionals to be non-negative definite.AMS 2000 Mathematics subject classification: Primary 39A12; 39A13. Secondary 34B24; 49K99

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