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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ONE THE SOURCES AND PROPAGATION
TWO ROOTFINDING FOR NONLINEAR
THREE INTERPOLATION THEORY
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accuracy algorithm arithmetic assume bound calculate Chapter Chebyshev coefficients column condition number constant continuously differentiable define denote derivation diagonal differential equations discussion divided difference eigenvalues eigenvectors estimate Euler's method evaluate Example Consider extrapolation finite forward difference function Gauss-Seidel method Gaussian elimination Gaussian quadrature given in Table implies initial guess initial value problem integrand interpolating polynomial interval iteration method least squares linear algebra linear system mathematical matrix norm matrix of order midpoint method multiplicity multistep methods Newton's method node points nonsingular nonzero notation numerical integration numerical methods numerical solution obtain orthogonal perturbations pivoting polynomial interpolation polynomial of degree rate of convergence Ratio relative error root rounding errors satisfy secant method Section significant digits Simpson's rule solution Y(x solve Ax speed of convergence spline stability stepsize symmetric Taylor series Taylor's theorem theory tion trapezoidal rule tridiagonal truncation error upper triangular variable zero