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THE REPRESENTATION OF NUMBERS
ALGORITHMS AND ERROR
CLASSICAL NUMERICAL ANALYSIS TO NEWTONS FORMULA
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algorithm Apply approximation arguments assuming boundary values Chebyshev Chebyshev polynomials choose coefficients collocation polynomial column computation constant convergence correct value corresponding cubic data points decimal places determined diagonal difference equation differential equation digits eigenvalues eigenvector equal error Euler Euler-Maclaurin formula Evaluate exact solution example factor five places follows formula of Problem found in Problem four places function y(x Gaussian Gaussian elimination given Hilbert matrix initial conditions interpolation interval iteration leads least-squares matrix maximum error method min-max minimum multiply Newton's Newton's method norm numbers obtain orthogonal parabola place accuracy polynomial of degree preceding problem previous problem produce Prove quadratic recursion relative error result Romberg's method root roundoff error Runge-Kutta Runge-Kutta method sequence Show Simpson's rule six places Solve spline step Substituting subtracting Suppose Table Taylor series theorem trapezoidal rule triple truncation error vector zero