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In the **conjugate-gradient method**, not a line, but rather a plane,
is searched.
A plane is made from an arbitrary linear combination of two vectors.
One vector will be chosen to be the gradient vector, say *g*.
The other vector will be chosen to be the previous descent step vector,
say *s* = *x*_{j} - *x*_{j-1}.
Instead of we need a linear combination,
say .For minimizing quadratic functions the plane search requires
only the solution of a two-by-two set of linear equations
for and .The equations will be specified here along with the program.
(For *nonquadratic * functions a plane search is considered intractable,
whereas a line search proceeds by bisection.)

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Stanford Exploration Project

10/21/1998