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The use of conjugate gradients helps to speed convergence by choosing a direction that is a linear combination of the past and current steepest descent vectors Luenberger (1984). Following Mora (1987), I use a conjugate gradient approach given by Polak and Ribiére (1969)
 
(10) 
where c_{n} is the conjugate gradient update. Note that this is equivalent to the formulation in Mora (1987) where data and model space covariances are represented by identity operators. Equation 5 thus modifies to
 

 (11) 
The computation of conjugate gradient direction in equation 11 comes essentially at no cost because the previous gradient vector, g_{n1}, easily can be stored in memory.
Next: Steplength Definition
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Stanford Exploration Project
1/16/2007