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-- bisection method for solving non-linear equations
function bisect(f,a,b,fa,fb)
write(n," a=",a," fa=",fa," b=",b," fb=",fb,"\n")
local c=(a+b)/2
if c==a or c==b then return c end
if abs(a-b)<delta then return c end
n=n+1
local fc=f(c)
if fa*fc<0 then return bisect(f,a,c,fa,fc) else return bisect(f,c,b,fc,fb) end
end
-- find root of f in the inverval [a,b]. bisection needs that f(a)*f(b)<0
function solve(f,a,b)
delta=1e-9 -- tolerance
n=0
local z=bisect(f,a,b,f(a),f(b))
write(format("after %d steps, root is %.10g, f=%g\n",n,z,f(z)))
end
-- our function
function f(x)
return x*x*x-x-1
end
solve(f,1,2)
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