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IllConditioningMeasures of Condition
7 other sections not shown
absolute value accuracy Appendix arithmetic Assume Chebyshev acceleration Cholesky coefficients complete positioning complex component computed conjugate convergence rate defined diagonal elements diagonal matrix direct methods eigenvalues eigenvectors error measure error vector Gaussian elimination given Hence Hermitian matrix ill conditioned integer inverse matrix iteration matrix iterative methods Jacobi method largest absolute eigenvalue linear equations linear system lower triangular main diagonal matrix inversion minimize multiplications n x n nonsingular matrix nonstationary number of iterations obtained orthogonal matrix parameters partial differential equations Peaceman-Rachford method permutations polynomial positive definite rate of convergence residual vector roundoff error row and column row interchanges scalar Section Seidel iteration Seidel method solution vector solving Ax spectral radius successive overrelaxation symmetric and positive symmetric matrix system Ax systems of linear Theorem Tk(y transformation triangular form triangular matrix tridiagonal unitary unitary matrix upper triangular written zero