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# Waveform applications of least squares

By the methods of calculus,
one learns to find the coordinates
of an extremal *point* on a curve.
In the calculus of variations,
one learns how to find extremal *functions*.
In practice,
the continuum may be approximated on a mesh
and the distinction blurs.
In the calculus of variations problems, however,
the matrices can be immense,
a disadvantage often partially offset by their orderly form.
In this chapter we will take up examples
in the use of least squares on waveforms and
relationships between groups of waveforms.
This leads to a massive full matrix called the
block-Toeplitz matrix for which we have a
special solution technique.

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Stanford Exploration Project

10/30/1997