Re: [Help-glpk] IRR (Internal Rate of Return) using MathProg

[Andrew Makhorin]

> It is well known, and your links show how, to use Newton's algorithm
> (aka Newton Raphson's algorithm) to find the IRR, since it's really
> find a root of a polynomial (see the other post by Jeffery Kantor,
> which also describes the fact that depending on the cash flows, there
> could be multiple solutions).
> 

Newton-Raphson's method is not a good choice in this case because 
i) it requires an initial guess, ii) it is able to find only one root;
iii) it may not converge. To find all roots of a polynomial it is much
better to use a specialized algorithm, for example, QD-algorithm or
Bairstow's algorithm. Note also that roots of polynomials of high degree
are extremely sensible to round-off errors in specifying the polynomial
coefficients, so I belive that there should exist another formulation 
of IRR.