                C++ Toolbox for Verified Computing I
                       Basic Numerical Problems

    Copyright (c) 1995 Rolf Hammer, Matthias Hocks, Dietmar Ratz

The function LinSolve(A,b) computes a verified solution to the square linear
system A*x=b for a real square matrix A and real vector b based on a
Newton-like method for an equivalent fixed-point problem.

The function returns a vector with entries [x;cond;err] where x represents
the verified enclosure or exact solution to the system, cond a condition
number estimate and err an eventual error message. The function linsys(A,b)
just returns the resulting vector enclosure.

   >A=1.*BoothroydDecker(6);b=[1;2;3;4;5;6];Precision(-10);
   >(1/A)*b
    [0;1;-2;3.0000000001;-4.0000000002;5.0000000005]
   >LinSolve(A,b)
    [[0;1;-2;3;-4;5];112890625.00085557;""]
   >A*linsys(A,b)-b
    [0;0;0;0;0;0]