2 x1+x2**2; 1.5*x1*x2+x2**2+x2**3; TITLE : decker3, one regular root and the origin is double Besides one regular root, the origin appears with multiplicity two. One deflation suffices. REFERENCES : D.W. Decker, H.B. Keller, C.T. Kelley: "Broyden's method for a class of problems having singular Jacobian at the root." SIAM J. Numer. Anal. 22, 566-574, 1985 THE SOLUTIONS : 3 2 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x2 : 1.93584189371047E-08 -3.76778264325582E-09 x1 : -2.57203498484257E-23 1.67296865319508E-23 == err : 2.313E-08 = rco : 4.625E-08 = res : 1.013E-15 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x2 : -6.79169984292363E-10 1.98506748476749E-10 x1 : 9.31975989016455E-28 -1.06749809400614E-27 == err : 8.777E-10 = rco : 1.755E-09 = res : 1.383E-18 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x2 : 2.00000000000000E+00 -5.93472984109987E-67 x1 : -4.00000000000000E+00 2.07715544438496E-66 == err : 2.506E-51 = rco : 1.325E-02 = res : 5.935E-67 ==