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Numerical Analysis as a Subject Area
Elementary Operations with Automatic Digital Computers
Surveillance of Number Ranges
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accuracy algorithm Apply arithmetic assume binary bounds Chapter coefficients compute continuous convergence defined Definition derivatives described determine differential equation eigenvalue evaluate Evidently exact example EXERCISES exists floating-point follows function f(x Gaussian quadrature given Hence Heun method initial-value problem integer interpolation formula interpolation points iterative method Lagrangian interpolation less let us consider linear interpolation matrix method based method of false method of undetermined Moreover Muller's method multiplicity Newton method numerical analysis numerical differentiation numerical quadrature numerical quadrature formulas obtain points x0 polynomial equation polynomial of degree polynomial P(x procedure proof real roots rectangle rule reduced polynomial reference set representation result root of 1.1 Runge-Kutta method satisfies secant method Section sequence significant digits Simpson's rule single-step error solving starting values Subroutine Taylor's theorem trigonometric polynomial undetermined weights unique polynomial unique solution vanish vector verify zero of/(x