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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 derivatives determined diagonal difference differential equations discretization error eigenvalues eigenvector elements estimate Euler's method exact solution example exists formula Gauss-Seidel method given hence Hermitian Hessenberg Hessenberg matrix initial-value problem integration interpolating polynomial interpolation problem interval iterative methods Jacobi method Jordan normal form linear equations method of order minimization multistep method n x n matrix Newton's method nonsingular 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 support points system of equations system of linear Theorem tion transformation triangular decomposition triangular matrix tridiagonal matrix uniquely unitary matrix upper triangular variables Wilkinson zero