An Introduction to Numerical Analysis
This Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated. New topics covered include optimization, trigonometric interpolation and the fast Fourier transform, numerical differentiation, the method of lines, boundary value problems, the conjugate gradient method, and the least squares solutions of systems of linear equations. Contains many problems, some with solutions.
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algebra algorithm applied arithmetic assume asymptotic error bound calculate Chapter Chebyshev coefficients condition continuously differentiable cubic define denote derivative differential equations digits discussion divided difference eigenvalues error estimate error formula Euler's method evaluate finite Gaussian elimination Gaussian quadrature give given in Table global error graph illustrated initial guess initial value problem integrand interpolating polynomial interval iteration methods least squares linear system mathematical matrix methods for solving midpoint method multiple multistep methods Newton's method node points nonlinear norm notation numerical analysis numerical integration numerical methods numerical solution obtain orthogonal perturbations pn(x polynomial interpolation polynomial of degree proof quadratic Ratio root rootfinding rounding errors Runge-Kutta methods satisfy secant method Section Shampine Simpson's rule solution Y(x stability Taylor's theorem Theorem theory tion trapezoidal method trapezoidal rule trunc truncation error unique variable vector Y(xn zero