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Golub and Loan (1980) phrased the TLS problem as follows. Given a forward
modeling operator **L** and measured data **d**, assume that both are contaminated
with white noise of uniform variance; matrix **N** and vector **n**, respectively.
Then the TLS solution is obtained by minimizing the Frobenius matrix norm of the
augmented noise matrix:
| |
(1) |

subject to the constraint that the solution is in the nullspace of the combined
augmented noise and input operators:
| |
(2) |

To solve the system of equations (1) and (2),
Golub and Loan (1980) introduced a technique based on the Singular Value
Decomposition (SVD). Although mathematically elegant, SVD-based approaches are
generally unrealistic for the large-scale problems that are the norm in exploration
geophysics.

** Next:** Equivalence with Rayleigh Quotient
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** Previous:** introduction
Stanford Exploration Project

11/11/2002