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Model fitting by least squares
HOW TO DIVIDE NOISY SIGNALS
Dividing by zero smoothly
Damped solution
Formal path to the low-cut filter
How much damping?
MULTIVARIATE LEAST SQUARES
Inside an abstract vector
Normal equations
Differentiation by a complex vector
From the frequency domain to the time domain
Unknown filter
Unknown input: deconvolution with a known filter
ITERATIVE METHODS
Sign convention
Method of random directions and steepest descent
Null space and gradient methods
Why steepest descent is so slow
Conjugate direction
Routine for one step of conjugate-direction descent
Setting up a generic solver program
Test case: solving some simultaneous equations
INVERSE NMO STACK
VESUVIUS PHASE UNWRAPPING
Digression: curl grad as a measure of bad data
Estimating the inverse gradient
Discontinuity in the solution
THE WORLD OF CONJUGATE GRADIENTS
Physical nonlinearity
Statistical nonlinearity
Coding nonlinear fitting problems
Standard methods
Understanding CG magic and advanced methods
REFERENCES
About this document ...
Stanford Exploration Project
2/27/1998
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