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Unformatted text preview: → one knows that ξ ≤ 1 / 4 for quadratics and ξ ≤ 1 for linears. Audet and Vicente (SIOPT 2008) Unconstrained optimization 66/109 Underdetermined polynomial models Consider a underdetermined quadratic polynomial model built with less than ( n + 1)( n + 2) / 2 points. Theorem If Y is C ( Y ) –poised for linear interpolation or regression then k∇ f ( y ) ∇ m ( y ) k ≤ C ( Y ) [ C ( f ) + k H k ] Δ ∀ y ∈ B ( x ; Δ) where H is the Hessian of the model.→ Thus, one should minimize the norm of H . Audet and Vicente (SIOPT 2008) Unconstrained optimization 67/109...
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 Spring '06
 Tapley
 Finance, Algebra, Polynomials, Numerical Analysis, Audet

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