<p> Davide Carpi </p>

7d531dc8-7dcc-4aeb-9289-29f3954066d7 37 6 9 decimal

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golden section search algorithm. # F a b ε maxIter target GoldenSearch φ 15 sqrt + 2 / : a b > x.lw b : x.up a : 21 line x.lw a : x.up b : 21 line if i 0 : d 2 φ - (x.up x.lw - (* : x.1 x.lw d + : x.2 x.up d - : f.x1 x.1 F : f.x2 x.2 F : i maxIter < x.up x.lw - abs ε ≤ break x.1 F x.2 F > (target min ≡ (& (x.1 F x.2 F < (target max ≡ (& | x.lw x.1 : x.1 x.2 : f.x1 f.x2 : x.2 x.up 2 φ - (x.up x.lw - (* - : f.x2 x.2 F : 51 line x.up x.2 : x.2 x.1 : f.x2 f.x1 : x.1 x.lw 2 φ - (x.up x.lw - (* + : f.x1 x.1 F : 51 line if i i 1 + : 21 line if 11 line while x.up x.lw + 2 / i 11 mat 21 mat 101 line :

x f 21 x 3^+ (* - x 2^7 - x 2^+ (* + :

x f x f 1.264 - 1.265 - f + 20 red 1 5 mat 2 1 sys

x f 1.5 - 1 - 105 -^50 min GoldenSearch 1.26556264377163 - 2311 mat 21 mat

x f 1 - 1105 -^50 max GoldenSearch 0.000001407168397 - 2611 mat 21 mat

x f 23105 -^50 min GoldenSearch 2.7655665452058 2411 mat 21 mat

The Mathcad code is not compatible with Smath

Analytical points from 'solve'

x D1 x f x diff :

x D2 x D1 x diff :

x f x D1 x D2 3 1 sys

x D1 x 1.3 - 2.8 solve 1.26556443264091 - 1.122032 109 -^* - 2.76556443311389 31 mat

x D1 x 1.5 - roots 1.26556443707463 -

x f x 2 - 4 solve 1.922518 - 3.852153 21 mat