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Stability Convergence and Accuracy
Boundary Value and Eigenvalue Problems
Vectors Matrices and Norms
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assume Chapter coefficients column compute condition number consider consistent with L[u convergence Corollary corresponding defined degree of approximation derivatives determine difference equation differential equation discrete operator discussion eigenvalues eigenvectors elementary divisors Euler method exact solution example EXERCISES exists function Gauss-Seidel method Gaussian elimination given Hence Hermitian Hessenberg Hessenberg matrix inner product integer Jacobi method Lemma Lh[u linear combination linear mapping linear N-step method linearly independent matrix norm mesh points method of order methods for solving midpoint method modulus Moreover multiplicative inverse nonnegative nonsingular obtain ordered basis Peaceman-Rachford points of Rh polynomial positive definite procedure proof is left Prove Theorem QR algorithm relative degree residue representation result roots satisfies scalar Section sequence similarity transformation SOR method stable starting values subspace sufficiently small symmetric matrix triangular unique solution vanish vector norm vector space Verify write zero