3 x1+x2+x3-1; 0.2*x1**3+0.5*x2**2-x3+0.5*x3**2+0.5; x1+x2+0.5*x3**2-0.5; TITLE : ojika3, needs one deflation with different systems This system has one root of multiplicity four and another root of multiplicity two. For both roots, one deflation suffices, but the deflated systems are different, as the numerical rank of the Jacobian matrix of the original system is different for different clusters. REFERENCES : T. Ojika, S. Watanabe, and T. Mitsui: "Deflation algorithm for the multiple roots of a system of nonlinear equations." J. Math. Anal. Appl. 96, 463-479, 1983. THE SOLUTIONS : 6 3 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -2.50000090252499E+00 2.90368755567384E-07 x2 : 2.50000135378748E+00 -4.35553133350855E-07 x3 : 9.99999548737505E-01 1.45184377783471E-07 == err : 3.578E-06 = rco : 1.729E-08 = res : 4.706E-13 == solution 2 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 7.75740356597569E-08 -3.82831846722857E-07 x2 : 5.98217505952537E-08 4.40213430502877E-07 x3 : 9.99999862604214E-01 -5.73815837800202E-08 == err : 1.155E-06 = rco : 3.605E-08 = res : 1.372E-13 == solution 3 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 4.27729624315320E-07 3.14383400896888E-07 x2 : -2.73579106519331E-08 -3.72418807599902E-07 x3 : 9.99999599628286E-01 5.80354067030143E-08 == err : 1.601E-06 = rco : 6.133E-08 = res : 1.244E-13 == solution 4 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -2.49999962963196E+00 -1.15854517911605E-07 x2 : 2.49999944444794E+00 1.73781776867394E-07 x3 : 1.00000018518402E+00 -5.79272589557885E-08 == err : 1.452E-06 = rco : 7.047E-09 = res : 7.837E-14 == solution 5 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 1.20590219602005E-07 -6.07683419190186E-07 x2 : 1.60140440371271E-07 4.84080555470448E-07 x3 : 9.99999719269340E-01 1.23602863719738E-07 == err : 1.777E-06 = rco : 6.520E-08 = res : 1.820E-13 == solution 6 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : 5.40928071143848E-08 8.10911604128108E-07 x2 : 2.69427735612677E-07 -4.22442959960439E-07 x3 : 9.99999676479457E-01 -3.88468644167669E-07 == err : 2.269E-06 = rco : 9.660E-08 = res : 2.368E-13 ==