## The essentials of numerical computation |

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### Contents

Some Fundamental Ideas in Numerical Computation | 1 |

Interpolation in Tabulated Functions | 25 |

Least Squares Approximation of Tabulated Functions and Data | 48 |

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### Common terms and phrases

accuracy algorithm apply approach arithmetic augmented matrix bisection calculation chapter column computed consider convergence cubic curve denotes diagonal differential equation dy/dx eigenvalue eigenvectors element error estimate Euler's method example EXERCISES expressed factors finite difference formula function f(x Gauss-Seidel Gaussian elimination given gives go to step gradient method Hence i i i+1 i+1 i+1 idea integral inverse involves iteration least squares approximation linear equations mathematical minimize minimum model function Newton's method nonlinear equations numerical obtain optimization order Runge-Kutta method polynomial problem procedure QR algorithm quadratic function relative error residuals result root rounding error Runge-Kutta method secant method shooting method significant figures simple Simpson's rule smallest eigenvalue solve the equations spline straight line Suppose tabulated function Taylor series technique trapezoidal rule upper triangular variables vector Write a program x-values y(x+h zero