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a. Show that the quadratic polynomial
P(α) = g1 + h1α + h3α (α − α2)
interpolates the function h defined in (10.18):
h(α) = g(x(0) − α∇g x(0))
at α = 0, α2, and α3.
b. Show that a critical point of P occurs at
α0 = 1/2 (α2 − h1 / h3). |
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