3 x1**2+x2+x3-1; x1+x2**2+x3-1; x1+x2+x3**2-1; TITLE : ojika2, two regular and three double roots, one deflation The system has two regular roots and three double roots, for which one deflation suffices. REFERENCES : T. Ojika: "Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations." J. Math. Anal. Appl. 123, 199-221, 1987. THE SOLUTIONS : 8 3 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 2.55401909702350E-07 1.15513090510306E-07 x2 : 2.55401909702350E-07 1.15513090510306E-07 x3 : 9.99999744598090E-01 -1.15513090510306E-07 == err : 1.113E-06 = rco : 4.856E-08 = res : 3.331E-13 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 4.14213562373095E-01 1.75240110224570E-57 x2 : 4.14213562373095E-01 6.57150413342137E-58 x3 : 4.14213562373095E-01 -2.38963786669868E-57 == err : 4.119E-16 = rco : 6.017E-02 = res : 3.331E-16 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 9.99999713390212E-01 -1.67781352689919E-07 x2 : 2.86609788584706E-07 1.67781352689919E-07 x3 : 2.86609788573014E-07 1.67781352689919E-07 == err : 1.363E-06 = rco : 7.573E-08 = res : 4.508E-13 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 1.00000002452496E+00 -1.19643680400072E-08 x2 : -2.45249649981224E-08 1.19643680400072E-08 x3 : -2.45249649194714E-08 1.19643680400072E-08 == err : 1.073E-07 = rco : 6.082E-09 = res : 3.093E-15 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -1.21703146098215E-08 5.43170638278471E-10 x2 : 1.00000001217031E+00 -5.43170638278467E-10 x3 : -1.21703147139869E-08 5.43170638278470E-10 == err : 2.170E-08 = rco : 2.119E-09 = res : 2.249E-16 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -1.89786129600717E-07 2.57827303828198E-07 x2 : 1.00000018978613E+00 -2.57827303828199E-07 x3 : -1.89786129720831E-07 2.57827303828198E-07 == err : 1.343E-06 = rco : 7.460E-08 = res : 3.847E-13 == solution 7 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -8.77948078949377E-08 -1.70530076619273E-07 x2 : -8.77948078949377E-08 -1.70530076619273E-07 x3 : 1.00000008779481E+00 1.70530076619274E-07 == err : 7.750E-07 = rco : 3.339E-08 = res : 1.540E-13 == solution 8 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -2.41421356237309E+00 -4.09243983395689E-111 x2 : -2.41421356237309E+00 -3.95902465688893E-111 x3 : -2.41421356237309E+00 -1.58010228437802E-110 == err : 1.507E-14 = rco : 4.142E-01 = res : 6.902E-110 ==