Subversion Repositories WoWGM

-- bisection method for solving non-linear equations

delta=1e-6	-- tolerance

function bisect(f,a,b,fa,fb)

 local c=(a+b)/2

 io.write(n," c=",c," a=",a," b=",b,"\n")

 if c==a or c==b or math.abs(a-b)<delta then return c,b-a 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]. needs f(a)*f(b)<0

function solve(f,a,b)

 n=0

 local z,e=bisect(f,a,b,f(a),f(b))

 io.write(string.format("after %d steps, root is %.17g with error %.1e, f=%.1e\n",n,z,e,f(z)))

end

-- our function

function f(x)

 return x*x*x-x-1

end

-- find zero in [1,2]

solve(f,1,2)