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pro vyhledávání: '"Robert Grone"'
Autor:
Robert Grone, Jose E. Castillo
Publikováno v:
Linear and Multilinear Algebra. 65:2031-2045
This paper describes how discrete versions of the derivative on the real line induce discrete version of the gradient and divergence in higher dimensions. This is geometrically motivated by results in algebraic graph theory since the grid in n dimens
Autor:
Robert Grone, Russell Merris
Publikováno v:
Linear Algebra and its Applications. 428(7):1565-1570
A graph that can be constructed from isolated vertices by the operations of union and complement is decomposable. Every decomposable graph is Laplacian integral. i.e., its Laplacian spectrum consists entirely of integers. An indecomposable graph is n
Autor:
Robert Grone, Jose E. Castillo
Publikováno v:
SIAM Journal on Matrix Analysis and Applications. 25:128-142
One-dimensional, second-order finite-difference approximations of the derivative are constructed which satisfy a global conservation law. Creating a second-order approximation away from the boundary is simple, but obtaining appropriate behavior near
Autor:
Robert Grone, Stephen Pierce
Publikováno v:
Linear and Multilinear Algebra. 41:63-79
Let A be an mn- by - mn symmetric matrix. Partition A into m 2 n - by - n blocks and suppose that each of these blocks is also symmetric. Suppose that for every decomposable (rank one) tensor ν ⊗ w, we have (ν ⊗ w) t A(ν otimes; w) ≥ 0. Here
Autor:
Robert Grone
Publikováno v:
Linear and Multilinear Algebra. 39:133-136
Let G be a simple graph on vertices V={1,…,n}, with Laplacian matrix L=L(G). suppose L has eigenvalues λ1≥…≥λn−0, and that the degree sequence of G is d 1≥…λd n. In this paper we provide an improvement to the majorization inequalitie
Autor:
Robert Grone, Russell Merris
Publikováno v:
SIAM Journal on Discrete Mathematics. 7:221-229
Let G be a graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then L(G) = D(G) - A(G) is the Laplacian matrix of G. The first section of this paper is devoted to properties of Laplacian integral graphs,
Publikováno v:
Linear Algebra and its Applications. 201:181-198
The problem we study concerns mn-by-mn real symmetric matrices A = [Aij]. The objective is to obtain best possible bounds on the spectrum of A given that the quadratic form on decomposable unit vectors in R has values restricted to the unit interval
Autor:
Robert Grone
Publikováno v:
Linear Algebra and its Applications. 150:167-178
Let G be a simple graph on n vertices, and let L be the Laplacian matrix of G. We point out some connections between the geometric properties of G and the spectrum of L. The multiplicities and eigenspaces as well as the eigenvalues of L are of geomet
Autor:
Robert Grone, Russell Merris
Publikováno v:
Graphs and Combinatorics. 6:229-237
LetG be a graph onn vertices. Denote byL(G) the difference between the diagonal matrix of vertex degrees and the adjacency matrix. It is not hard to see thatL(G) is positive semidefinite symmetric and that its second smallest eigenvalue,a(G) > 0, if
Publikováno v:
Linear Algebra and its Applications. 134:63-70
Let R n denote the convex, compact set of all real n -by- n positive semidefinite matrices with main-diagonal entries equal to 1. We examine the extreme points of R n focusing mainly on their rank. the principal result is that R n contains extreme po