## Iterative Solution of Nonlinear Equations in Several VariablesIterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in 1970, it offers a research-level presentation of the principal results known at that time. Although the field has developed since the book originally appeared, it remains a major background reference for the literature before 1970. In particular, Part II contains the only relatively complete introduction to the existence theory for finite-dimensional nonlinear equations from the viewpoint of computational mathematics. Over the years semilocal convergence results have been obtained for various methods, especially with an emphasis on error bounds for the iterates. The results and proof techniques introduced here still represent a solid basis for this topic. |

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### Contents

CL30_pt1 | 8 |

CL30_ch1 | 9 |

CL30_ch2 | 34 |

CL30_ch3 | 59 |

CL30_pt2 | 91 |

CL30_ch4 | 93 |

CL30_ch5 | 119 |

CL30_ch6 | 147 |

CL30_pt4 | 279 |

CL30_ch9 | 281 |

CL30_ch10 | 299 |

CL30_ch11 | 347 |

CL30_pt5 | 381 |

CL30_ch12 | 383 |

CL30_ch13 | 432 |

CL30_ch14 | 473 |

### Other editions - View all

Iterative Solution of Nonlinear Equations in Several Variables J. M. Ortega,W. C. Rheinboldt Limited preview - 1970 |

Iterative Solution of Nonlinear Equations in Several Variables J. M. Ortega,W. C. Rheinboldt Limited preview - 2014 |

### Common terms and phrases

Akad applied arbitrary Assume that F Banach spaces boundary value problems compact Comput consider continuously differentiable convex functionals convex set critical point D C R defined diagonal differential equations Dokl eigenvalues ensures example exists F is continuous fixed point follows functional g G-derivative g(xk given Gºx Hence holds homeomorphism implies isotone iterative methods iterative processes lemma Let F Let g limº M-matrix mapping F Math matrix monotone Moreover Newton iteration Newton's method nonlinear nonlinear equations nonsingular norm NOTES AND REMARKS obtain one-step open neighborhood open set point of attraction point of G positive definite Proof quadratic rate of convergence result Rheinboldt satisfies secant method sequence xk set Do CD Show solution of nonlinear Suppose that G symmetric theorem two-point unique solution vectors wk+1 x e Rº