منابع مشابه
On eigenvalues of Seidel matrices and Haemers' conjecture
For a graph G, let S(G) be the Seidel matrix of G and θ1(G), . . . , θn(G) be the eigenvalues of S(G). The Seidel energy of G is defined as |θ1(G)| + · · · + |θn(G)|. Willem Haemers conjectured that the Seidel energy of any graph with n vertices is at least 2n − 2, the Seidel energy of the complete graph with n vertices. Motivated by this conjecture, we prove that for any α with 0 < α < 2, |θ1(...
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For Ax = b, it has recently been reported that the convergence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type P = I + S (α) to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this paper, we discuss the adaptive Gauss-Seidel iterative method which uses P = I + S (α) + K̄ (β) as a preconditioner. We present some com...
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We show that for certain systems of linear equations with coefficient matrices of Hessenberg form it is possible to use Gaussian elimination to obtain an extrapolated version of the Gauss-Seidel iterative process where the iteration matrix has spectral radius zero. Computational aspects of the procedure are discussed.
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The purpose of this note is to investigate the close relationship that exists between the Euler-Seidel matrix [3, 4, 5, 6, 10] of an integer sequence, and the Hankel matrix [9] of that sequence. We do so in the context of sequences that have integral moment representations, though many of the results are valid in a more general context. While partly expository in nature, the note assumes a cert...
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We describe the implementation and performance of an e cient parallel Gauss-Seidel algorithm that has been developed for irregular, sparse matrices from electrical power systems applications. Although, Gauss-Seidel algorithms are inherently sequential, by performing specialized orderings on sparse matrices, it is possible to eliminate much of the data dependencies caused by precedence in the ca...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2018
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2017.10.009