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The TLS solution is closely related to the classic damped least squares (DLS)
solution, where the damping factor, , is the smallest nonzero singular value
of the augmented matrix :
| |
(4) |

The TLS solution can be rewritten Björck (1996); Golub and Loan (1980) as follows.
| |
(5) |

The only difference between equations (4) and (5)
is the negative sign on the damping term. Thus the TLS problem is considered a
``deregularization'' of the standard LS problem, and is guaranteed to be worse
conditioned, since is positive-semidefinite at worst Björck (1996).

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Stanford Exploration Project

11/11/2002