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NUMERICAL DIFFERENTIATION NUMERICAL QUADRATURE
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abscissas accuracy algorithm analogous arithmetic assume bound calculate Chap Chebyshev polynomials coefficients column composite rules consider convergence corrector corresponding deduce defined derive determine diagonal difference differential equation digital computer discussed eigenvalues eigenvectors elements equal error term estimate evaluation exact for polynomials Example Gaussian quadrature given Householder's method interval a,b Jacobi method Lagrangian interpolation formula least-squares approximation linear magnitude matrix maximum error multiple Newton-Cotes formulas notation numerical analysis numerical differentiation numerical integration numerical integration method orthogonal polynomials polynomial of degree positive predictor predictor-corrector methods previous problem quadrature formula rational function recurrence relation results of Prob right-hand side root roundoff error Runge-Kutta methods satisfied secant method sequence solve stability step subintervals symmetric Table tabular points technique Theorem tion trapezoidal rule true solution true value truncation error vector weight function zero