2 x1**3+x1*x2; x2**2+x2; TITLE : decker1, with three regular roots and one triple root The system has three regular roots and the origin is a triple root for which two deflations are needed. REFERENCES : D.W. Decker, C.T. Kelley: "Newton's method at singular points. II" SIAM J. Numer. Anal. 17, 465-471, 1980 THE SOLUTIONS : 6 2 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -1.00000000000000E+00 0.00000000000000E+00 x2 : -1.00000000000000E+00 0.00000000000000E+00 == err : 0.000E+00 = rco : 4.000E-01 = res : 0.000E+00 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -4.68237338654844E-06 7.84924377521673E-06 x2 : 0.00000000000000E+00 0.00000000000000E+00 == err : 6.266E-06 = rco : 3.396E-10 = res : 7.955E-16 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 0.00000000000000E+00 0.00000000000000E+00 x2 : -1.00000000000000E+00 0.00000000000000E+00 == err : 0.000E+00 = rco : 1.000E+00 = res : 0.000E+00 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -2.95529258749206E-06 -5.31655257281928E-06 x2 : 0.00000000000000E+00 0.00000000000000E+00 == err : 4.136E-06 = rco : 1.529E-10 = res : 2.358E-16 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 1.00000000000000E+00 0.00000000000000E+00 x2 : -1.00000000000000E+00 0.00000000000000E+00 == err : 0.000E+00 = rco : 4.000E-01 = res : 0.000E+00 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 9.11529253275207E-06 1.25430449151191E-07 x2 : 0.00000000000000E+00 0.00000000000000E+00 == err : 4.620E-06 = rco : 2.561E-10 = res : 7.882E-16 ==