## Collected problems in numerical methods: An educational aid for students in universities and technical colleges |

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### Contents

The approx1mate solut1on of nonl1near algebra1c | 1 |

The solution of systems of nonlinear equations | 15 |

The calculation of eigenvalues and eigenvectors of matrices | 45 |

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### Common terms and phrases

accuracy of 10-5 approximate solution augmented matrix boundary conditions calculated CC Ol characteristic equation coefficients Continuation of 26 corresponding eigenvector cos2 denote determine the eigenvalues eigenvalues and eigenvectors equations THEORY Consider Euler's method five significant places following differential equations following matrices following systems Gauss-Seidel method Gaussian elimination greatest positive root H CM H Ol initial approximation interval inverse matrix IQ Ol Iterative methods Krylov's method length h Leverrier's method linear algebraic modified Euler-Cauchy method Newton's method Numerical Analysis numerical methods Ol 10 Ol Ol H Ol Ol Ol order Runge-Kutta formulae pivotal row polynomial recurrence relations Runge-Kutta method six significant places smallest positive root solve the following step length successive approximations systems of equations Tabulated values Taylor series Tf H Tf Ol triangular matrix upper triangular vector x3 xi