By using the next generation method and used

spectral radius (Van den Driessche and Watmough,2002).

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spectral radius as a measure of variation in node degree for complex network graphs.

This method is efficient for solving system of linear equations but, however, does not converge for some systems when the

spectral radius is greater than one.

The real part of the eigenvalues of these two last matrices are included in the interval (0, 1) with a

spectral radius smaller than 1 .

We also assume that u is strictly positive such that the

spectral radius of the Jacobian [P.

Mallios proved in 1986 that a Q-algebra is characterized by a zero neighbourhood consisting of elements normalized by means of the

spectral radius [11, p.

According with the theory, the method converges if, and only if, the

spectral radius of the iteration matrix, defined as the maximum absolute value of the matrix eigenvalues, is smaller than one.

g) the topological

spectral radius pt is upper semicontinuous;

We call the largest eigenvalue of L(G) the Laplacian

spectral radius of the graph G, denoted by [mu](G).

The techniques currently available in the literature are mostly based on Lyapunov's direct method [1], contraction mapping method [2], nonlinear measure method [3,4], nonlinear

spectral radius method [5] and so on.

A variant of ADI method involving the computational parameter with the diagonal part of A studied in section 2 and the

spectral radius of it is also obtained in terms of eigen values of the matrices occurring in the coefficient matrix A in the same section.

Therefore, we suggest as a second method to optimize the

spectral radius of the multigrid iteration matrix.