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The adjoint operator projects the data space back to the
model space and is defined by the dot product test
| |
(27) |

for any and . The method of conjugate gradients is
a particular case of the method of conjugate directions, where the
initial search direction is
| |
(28) |

This direction is often called the *gradient,* because it
corresponds to the local gradient of the squared residual norm with
respect to the current model . Aligning the initial
search direction along the gradient leads to the following remarkable
simplifications in the method of conjugate directions.

** Next:** Orthogonality of the gradients
** Up:** Fomel: Conjugate directions
** Previous:** ALGORITHM
Stanford Exploration Project

11/12/1997