> Can you please suggest a fast GSL method / algorithm to find the solutions > of a quadratic 3d system of algebraic equations? > > In the reduced form all 3 equations have zero on the l.h.s., and on the > r.h.s. there are constant, linear and quadratic terms composed of x1, x2, > x3 (the three variables).
Newton iteration, especially if you provide analytic Jacobian, should do well here. There may be faster things that can return multiple solutions, however. - Rhys
