First Principles of Numerical Analysis: An Undergraduate Text |
Contents
Applications of Taylors Theorem Part 1 | 19 |
Applications of Taylors Theorem Part 2 | 33 |
The Theory of Interpolation | 55 |
Copyright | |
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a₁ algorithm approximation arithmetic assume b₁ b₁(x called Chapter Chebyshev nodes coefficients complete pivoting compute convergence distinct points error example EXERCISES Section f(xn f₁ false position Fetch fi+1 finite flow diagram formula functional evaluations Gaussian elimination Gaussian quadrature given Hermite interpolation integration rule interchange interval iteration Lagrange interpolating polynomial least squares Lemma Let P(x linear system machine method of false multi-point methods multi-step methods Newton's method numerical analysis O(h² obtained p₁ partial pivoting piecewise polynomial interpolation polynomial of degree polynomial P(x predictor-corrector problem Proof r₁ rectangle rule Richardson extrapolation scaling sequence Simpson's rule single step methods solution solve Suppose system of equations Taylor's theorem tion trapezoidal rule triangular decomposition value theorem vanishes Wendroff x₁ x₁)² Xi+1 Xk+1 xn+1 Y₁ Y₂+1 zero