You need to specify to what accuracy you want the approximation. Usually a good method to begin working from is plain old schoolroom secant method. If you wanted very high accuracy, it might be worth looking at switching to a higher-order method once the iteration is well under way. However, choosing a suitable iteration is the easy part --- trickier is finding a good starting point in the first place. In this case it would help to have bounds on the constants a,b,c if possible: for example, if we knew they were close to unity, or alternatively quite large, it would be easier to make an intelligent initial guess. Fred Lunnon On 2/2/07, Christian Boyer <cboyer@club-internet.fr> wrote:
Sorry, some mistakes in my previous hypothesis.
With the 5th-degree equation:
x(x² + a)(x² + b) = c
x, a, b, c real numbers a, b > 0 c > (1+a)(1+b) x > 1
what is the fastest method to get an approximated value of x? (very few steps)
Christian.