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Topics in Integration
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algorithm approximate values arbitrary assume boundary-value problem calculation characteristic polynomial coefficients column computed convergence corresponding defined denote determined diagonal difference differential equations discretization error eigenvector elements estimate Euler's method exact solution example exists extrapolation methods formula Gauss-Seidel method given h(xk hence Hermitian Hessenberg Hessenberg matrix initial-value problem integration interpolating polynomial interval iterative methods Jacobi method Jordan normal form linear equations matrix norm method of order minimization multistep method n x n matrix Newton's method nonsingular norm numerically stable obtained orthogonal parameters partition pivot selection positive definite Proof QR method recursion Reinsch relative error roots roundoff errors satisfies Section sequence shooting method solution y(x solving spline function step system of equations system of linear Theorem tion transformation triangular decomposition triangular matrix tridiagonal matrix uniquely unitary matrix vector Wilkinson zero