8cea43cf-1427-4362-9706-e955e71142cb 6 3 5 decimal

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Mesh U,  within the bounds L, H L H N xd N intervals U 0 : dx H L - N / : i 1 N 1 + range U i el L dx i * dx - (+ : for U 51 line :

Min/Max of non-monotonic data sets

L 3 - :

H 4 :

N 100 :

We discretize a non monotonic f to simulate a real data set. Golden Ratio supports Smath linterp(vx,vy,x)

u L H N xd :

x Φ x 4^2 x 3^* - 7 x 2^* - 2 - :

the simulated data set data u u Φ vectorize augment :

The Golden-Ratio search [min/max]

x f u u Φ vectorize x linterp : a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : 21 line

ε 106 -^:

Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema y1 y2 ≥ max in range ≡ y1 y2 ≤ min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / iter 21 mat 61 line :

1. All modules/functions either "Symbolic/Numeric". 2. Once in target: shrink the range 3. respect the search y1 ≥ y2 ≡ "max in range" y1 ≤ y2 ≡ "min in range"

X f 1.5 - 1 - y1 y2 ≤ ε Extrema 1 el f 0.25 - 0.25 y1 y2 ≥ ε Extrema 1 el f 2.5 3 y1 y2 ≤ ε Extrema 1 el 31 mat :

X X 1 el f X 2 el f X 3 el f 31 mat 12 mat 1.25 - 0.01 2.74 31 mat 6.59 - 2.001 - 39.331 - 31 mat 12 mat

x f X 1 el X 1 el f + 15 red X 2 el X 2 el f + 15 red X 3 el X 3 el f + 15 red 3 5 mat 2 1 sys