An Introduction to Numerical AnalysisWiley, 1978 - 587 pagine 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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accuracy algorithm arithmetic assume asymptotic error formula bound calculate Chapter Chebyshev coefficients column condition number continuously differentiable define degree of precision denote derivation diagonal differential equations discussion divided difference eigenvalues eigenvectors estimate Euler's method evaluate finite function f(x Gauss-Seidel method Gaussian elimination Gaussian quadrature give given in Table illustrate implies initial guess integrand integration formula interval iteration method least squares approximation linear system matrix norm maximum minimax approximation multiplicity multistep methods Newton's method node points notation numerical integration numerical methods obtain orthogonal perturbations pivoting polynomial interpolation polynomial of degree proof Ratio relative error root rounding errors satisfy secant method Section Simpson's rule stability stepsize symmetric Taylor series Taylor's theorem Theorem theory tion trapezoidal rule tridiagonal truncation error upper triangular variable weight function Wilkinson x₁ xn+1 yn+1 zero