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fsolve or nSolve with the option falsepos_solver

The "false position" algorithm is an iterative algorithm based on linear interpolation : we compute the value of f at the intersection of the line (a, f (a)), (b, f (b)) with the x axis. This value gives us the part of the interval containing the root, and on which a new iteration is performed.
The convergence is linear but generically faster than bisection.
Input :
fsolve((cos(x))=x,x,-1..1,falsepos_solver)
Output :
[0.739085133215,0.739085133215]



giac documentation written by Renée De Graeve and Bernard Parisse