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_ _ CHAPTER applied assume block Gauss-Seidel block Jacobi matrix Chebyshev polynomials commute completes the proof Corollary corresponding cosh cyclic of index defined denote diagonal blocks difference equations Dirichlet problem eigen eigenvalue eigenvector essentially positive estimates exp(tQ fl[B Gauss-Seidel iterative Gauss-Seidel matrix Gauss-Seidel method h-consistent initial vector Jacobi iteration matrix Jacobi method ji[B jl(A jl[B Jordan canonical form Lemma lower triangular matrix Math matrices H matrix associated matrix problem mesh points method of iteration method with respect modulus 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 relaxation method result satisfies spectral radius Stieltjes matrix strict inequality successive overrelaxation iterative successive overrelaxation matrix sufficiently small symmetric and positive tridiagonal u(tQ zero