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Question: DirectSearch finds nonexisting roots

Question:DirectSearch finds nonexisting roots

Ali Guzel 70 Maple 2018
rootfinding directsearch
May 03 2022
2

DirectSearch finds nonexisting roots....     DirectSearch_finds_nonexisting_roots.mw

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restart
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plot([cos(x), 0.001*x*x],x=-40..40,y=0..2)     ### test function plot

 
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eq:= cos(x)= 0.001*x*x;     ###   float

cos(x) = 0.1e-2*x^2

 (1)
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use RealDomain in solve(eq,x,explicit) end use   ## lacking some of the roots

-7.793210110, 7.793210110, -11.11953559, 11.11953559, -4.734809278, 4.734809278, -1.568336644, 1.568336644

 (2)
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use RealDomain in solve(eq,x) end use

-7.793210110, 7.793210110, -11.11953559, 11.11953559, -4.734809278, 4.734809278, -1.568336644, 1.568336644

 (3)
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fsolve(eq,x=-30)

-31.17938383

 (4)
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plot([cos(x), 0.001*x*x],x=-32..-31,y=0.9..1)

 
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fsolve(eq,x=-32..-30);  fsolve(eq,x=-31.7..-31.4)

-31.17938383

  

-31.52634294

 (5)
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with(DirectSearch)

[BoundedObjective, CompromiseProgramming, DataFit, ExponentialWeightedSum, GlobalOptima, GlobalSearch, Minimax, ModifiedTchebycheff, Search, SolveEquations, WeightedProduct, WeightedSum]

 (6)
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eq;
SolveEquations(eq,AllSolutions):

cos(x) = 0.1e-2*x^2

 (7)
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interface(rtablesize=90);
SolveEquations(eq, AllSolutions)

90

  

Matrix(%id = 4800942722)

 (8)

DirectSearch finds nonexisting roots!!!

Dr. Ali GÜZEL

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