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Continuing by induction the process of adding a linear combination of
the previous steps to the arbitrarily chosen direction (known in mathematics as the *Gram-Schmidt orthogonalization
process*), we finally arrive at the complete definition of the new
step , as follows:
| |
(22) |

Here the coefficients are defined by equations
| |
(23) |

which correspond to the orthogonality principles
| |
(24) |

and
| |
(25) |

It is these orthogonality properties that allowed us to optimize the
search parameters one at a time instead of solving the *n*-dimensional
system of optimization equations for and .

** Next:** ALGORITHM
** Up:** IN SEARCH OF THE
** Previous:** Second step of the
Stanford Exploration Project

11/12/1997