## Numerical analysis |

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### Contents

Linear algebraic equations | 8 |

Nonlinear algebraic equations | 43 |

Eigenvalues and eigenvectors | 71 |

Copyright | |

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### Common terms and phrases

algorithm back substitution bisection boundary value problem bracketing interval calculated coefficient matrix column computed consider the solution Construct corresponding cubic spline data points deduce defined deflation denote derivatives diagonally dominant differential equation divided difference eigenvalues eigenvalues and eigenvectors eigenvectors elements evaluations exact value EXERCISE false position method following data formula forward difference Gauss elimination Gauss-Seidel method gives graph illustrate initial value problem integration interchanges interpolating polynomial inverse iteration Jacobi method Lagrange least squares approximation linear equations linear multistep method lower triangular LU decomposition multiple n x n Newton-Cotes formulas Newton's method non-linear obtained orthogonal partial pivoting piecewise polynomial of degree QR method quadrature rule rearranged roots rounding errors Runge-Kutta method sequence Simpson's rule solve subintervals symmetric matrix system of equations techniques term trapezium rule tridiagonal truncation error upper Hessenberg upper triangular vector x)dx zero