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We can define a minimizing problem that aims at finding by minimizing the following cost function:
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(47) |

The Newton iterative algorithms can be used for solving the minimizing problem. The standard Newton iterative algorithm is
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(48) |

However, the inverse of the Hessian is difficult to calculate. The Quasi-Newton algorithms are used commonly. The inverse of the Hessian matrix can be calculated with the DFP formula:
| |
(49) |

where , and .
The Quasi-Newton iterative algorithm is

| |
(50) |

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Stanford Exploration Project

11/1/2005