An Introduction to Numerical AnalysisThis 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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Page 277
Kendall Atkinson. Table 5.11 Gaussian quadrature for ( 5.1.11 ) n 2 34 In - 12.33621046570 - 12.12742045017 - 12.07018949029 - 12.07032853589 5 6 - 12.07034633110 7 - 12.07034631753 8 -12.07034631639 I - In 2.66E ... GAUSSIAN QUADRATURE 277.
Kendall Atkinson. Table 5.11 Gaussian quadrature for ( 5.1.11 ) n 2 34 In - 12.33621046570 - 12.12742045017 - 12.07018949029 - 12.07032853589 5 6 - 12.07034633110 7 - 12.07034631753 8 -12.07034631639 I - In 2.66E ... GAUSSIAN QUADRATURE 277.
Page 281
... Programs should be written containing these weights and nodes for standard values of n , for example , n = 2 , 4 , 8 , 16 , ... , 512 [ taken from Stroud and Secrest ( 1966 ) ] . 2 . 3 . 4 . 5 . In addition GAUSSIAN QUADRATURE 281.
... Programs should be written containing these weights and nodes for standard values of n , for example , n = 2 , 4 , 8 , 16 , ... , 512 [ taken from Stroud and Secrest ( 1966 ) ] . 2 . 3 . 4 . 5 . In addition GAUSSIAN QUADRATURE 281.
Page 308
Kendall Atkinson. Gaussian quadrature In Section 5.3 , we developed a general theory for Gauss- ian quadrature formulas a n ' w ( x ) f ( x ) dx = Σ wj , nf ( xj , n ) - j = 1 n≥ 1 that have degree of precision 2n 1. The construction of ...
Kendall Atkinson. Gaussian quadrature In Section 5.3 , we developed a general theory for Gauss- ian quadrature formulas a n ' w ( x ) f ( x ) dx = Σ wj , nf ( xj , n ) - j = 1 n≥ 1 that have degree of precision 2n 1. The construction of ...
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a₁ algorithm applied approximation arithmetic assume asymptotic error b₁ bound calculate Chapter Chebyshev coefficients column continuously differentiable define denote derivative digits discussion eigenvalues eigenvectors error estimate error formula Euler's method evaluate f(xn finite function f(x Gaussian elimination Gaussian quadrature give given in Table global error initial value problem integrand interval least squares linear system mathematical matrix norm midpoint method minimax multiplicity multistep methods Newton's method node points nonlinear notation numerical analysis numerical integration numerical methods numerical solution O(h² obtain ordinary differential equations orthogonal perturbations pivoting polynomial interpolation polynomial of degree proof Ratio root rounding errors Runge-Kutta methods satisfy Section Shampine Simpson's rule solution Y(x spline stability symmetric Theorem theory tion trapezoidal method trapezoidal rule trunc truncation error variable vector x₁ Xn+1 Y(xn y₁ Yn+1 zero λ₁ хо