## Advanced numerical analysis |

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### Contents

Errors in Matrix Inversion | 16 |

Iteration Schemes | 20 |

Solutions of NonLinear Equations | 31 |

6 other sections not shown

### Common terms and phrases

accumulated truncation error analytic function approximate arbitrary assume Bernoulli's method bounded circle coefficients common zero components compute consider convergence Cramer's Rule curve define determinant diagonal diffe difference equation difference quotients difference scheme domain of dependence eiax eigenvalues eigenvectors estimate f(x+l f(xk follows Fourier gives heat equation Hence hyperbolic implies inhomogeneous initial conditions initial data initial values integral iteration scheme lattice points matrix Max v(P maximum principle Moreover N(ax natural norm Newton's method number of steps number of zeros obtain Partial Differential Equation polynomial polynomial of degree positive definite problem recursion formula rence equation require roots of P(X round off error satisfy sin2 solu solution solve sufficiently small symmetric system of equations theorem tion uniformly unit circle utilizing v(x,t+k v(x+h,t variable vector x-axis xk+1