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We often need to damp the solutions to least squares problems.
We have a fitting problem (regression) with the two goals:
| |
(5) |

| (6) |

where is a roughening operator.
How big should be?
Suppose in human terms we'd like ``half''
the properties of the solution to come from the fitting
and ``half'' to come from the damping.
How might we define what we mean by ``half''?
We can start by considering balancing the two residual vectors
and .
| |
(7) |

Another approach is to balance the gradients.
The gradient is the ``force'' on the solution *m*.
| |
(8) |

where is the transpose of and likewise for .I suspect that is the better choice for but a little more experience would add confidence.

** Next:** ROW PARTITIONED OPERATORS
** Up:** Claerbout: Preconditioning and scalingPreconditioning
** Previous:** ROUGHENERS AND SMOOTHERS
Stanford Exploration Project

11/11/1997