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(...

The objective of this paper is to analyse the application of the Half-Sweep Gauss-Seidel (HSGS) method by using the Half-sweep approximation equation based on central difference (CD) and repeated trapezoidal (RT) formulas to solve linear fredholm integro-differential equations of first order. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and HalfSweep Gauss-Seidel (HS...

: In this retrospective study 48 humeral shaft fractures in 48 patients were operated on using the Seidel interlocking nail. The length of follow-up ranged from 6 to 60 months (median, 26 months). The treatment of fractures was satisfactory with the Seidel nail, but we emphasize the importance of countersinking the tip of the nail into the humeral head to avoid impingement. In 5 of 12 patients ...

We have recently considered decomposing a system of nonlinear equations by defining new variables corresponding to the intermediate results in the evaluation process. In that previous work, we applied both a derivative-free component solution process and an interval Gauss–Seidel method to the large, sparse system of equations so obtained. An analysis of the component solution process indicates ...

respectively. There are many iterative methods such as GMRES [7] and Bi-CGSTAB [9] algorithms for solving Eq. (1.1) which are more efficient than the Jacobi and Gauss-Seidel methods. However, when these methods are combined with the more efficient methods, for example as a preconditioner, can be quite successful. For example see [4, 6]. It has been proved that if A is a strictly diagonally domi...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...