Quoting Fred lunnon <fred.lunnon@gmail.com>:
Several authors have analysed the pitfalls involved in the numerical evaluation of the traditional schoolroom solution of a quadratic equation in one variable x: a x^2 - 2 b x + c = 0 ; x = (b + d)/a , (b - d)/a , where d^2 = b^2 - a c .
You wouldn't think that such a simple formula would cause such trouble, but I finally understood the source when I graphed the roots as functions of the coefficients - or rather the coefficients as functions of the roots. A family of straight lines intersects a family of hyperbolas, trouble arising near the case of equal roots where the intersections are tangencies. Such a picture would be a nice adjunct to a numerical analysis book - for those who like to see pictures illustrating their mathematics. -hvm ------------------------------------------------- www.correo.unam.mx UNAMonos Comunicándonos