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  1. -- bisection method for solving non-linear equations
  2.  
  3. delta=1e-6      -- tolerance
  4.  
  5. function bisect(f,a,b,fa,fb)
  6.  local c=(a+b)/2
  7.  io.write(n," c=",c," a=",a," b=",b,"\n")
  8.  if c==a or c==b or math.abs(a-b)<delta then return c,b-a end
  9.  n=n+1
  10.  local fc=f(c)
  11.  if fa*fc<0 then return bisect(f,a,c,fa,fc) else return bisect(f,c,b,fc,fb) end
  12. end
  13.  
  14. -- find root of f in the inverval [a,b]. needs f(a)*f(b)<0
  15. function solve(f,a,b)
  16.  n=0
  17.  local z,e=bisect(f,a,b,f(a),f(b))
  18.  io.write(string.format("after %d steps, root is %.17g with error %.1e, f=%.1e\n",n,z,e,f(z)))
  19. end
  20.  
  21. -- our function
  22. function f(x)
  23.  return x*x*x-x-1
  24. end
  25.  
  26. -- find zero in [1,2]
  27. solve(f,1,2)
  28.