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_ _ CHAPTER applied assume block Gauss-Seidel block Jacobi matrix block matrix Chebyshev polynomials Chebyshev semi-iterative method commute completes the proof Corollary corresponding cosh cyclic of index defined denote diagonal blocks difference equations Dirichlet problem eigen eigenvalue eigenvector essentially positive estimates Gauss-Seidel iterative Gauss-Seidel matrix Gauss-Seidel method h-consistent implies initial vector Jacobi iteration matrix Jacobi method jl(A Jordan canonical form Lemma Math matrices H matrix associated matrix problem mesh points method of iteration method with respect modulus N X N non-negative and irreducible non-negative matrices non-singular non-zero numerical approximation numerical solution optimum relaxation factor overrelaxation iterative method positive definite positive diagonal entries positive diagonal matrix positive real primitive primitive matrix Q is essentially rate of convergence real eigenvalues real numbers result satisfies spectral radius Stieltjes matrix strict inequality successive overrelaxation iterative successive overrelaxation matrix sufficiently small symmetric and positive tridiagonal u(to zero