On 23 Jun 2006 08:22:23 -0700, "C6L1V@shaw.ca" <C6L1V@shaw.ca> wrote:
>firstname.lastname@example.org wrote: >> Hi Folks, >> >> I am interested in the equation of form: >> a1*x1+a2*x2+a3*x3+...an*xn + b = 0 >> where "a1...an" and "b" are given and "x1...xn" are n unknown >> variables. Obviously, the system has n unknowns and only one equation. >> This equation comes with a set of constraints of form: >> -1<xi<1 where i = 1, ...n. > >Do you really mean -1 < xi < 1, or do you actually mean -1 <= xi <= 1? >This makes a tremendous difference. With non-strict inequalities, you >have an extensive and powerful theory of linear programming available >to you, but with strict inequalities this is not the case. It is >possible that your problem has no solution at all if you use "<", but >has easily-obtained solutions if you use "<=".
It's not an optimization problem. Of course there are solutions if sum_i |a_i| > |b|.