Model fitting by least squares |

**Jon Claerbout**

The first level of computer use in science and engineering is **modeling**.
Beginning from physical principles and design ideas,
the computer mimics nature.
Then the worker looks at the result, thinks a while,
alters the modeling program, and tries again.
The next, deeper level of computer use is that the computer
examines the results of modeling and reruns the modeling job.
This deeper level
is variously called
``**fitting**,''
``**estimation**,'' or
``**inversion**.''
We inspect the **conjugate-direction method** of fitting
and write a subroutine for it that is used in most of
the examples in this book.

- UNIVARIATE LEAST SQUARES
- Dividing by zero smoothly
- Damped solution
- Smoothing the denominator spectrum
- Imaging
- Formal path to the low-cut filter
- The plane-wave destructor

- MULTIVARIATE LEAST SQUARES
- Inside an abstract vector
- Normal equations
- Differentiation by a complex vector
- From the frequency domain to the time domain

- KRYLOV SUBSPACE ITERATIVE METHODS
- Sign convention
- Method of random directions and steepest descent
- Why steepest descent is so slow
- Null space and iterative methods
- The magical property of the conjugate direction method
- Conjugate-direction theory for programmers
- Routine for one step of conjugate-direction descent
- A basic solver program
- Fitting success and solver success
- Roundoff
- Test case: solving some simultaneous equations

- INVERSE NMO STACK
- FLATTENING 3-D SEISMIC DATA

- VESUVIUS PHASE UNWRAPPING

- OPERATOR SCALING (BINORMALIZATION)
- THE WORLD OF CONJUGATE GRADIENTS

- About this document ...

2014-12-01