###############################################################
# Building 'newt2' and sample output on lnx1.
#
# Note how different roots are found depending on the initial
# guess and how, in each case, convergence of both dx and
# the residual is quadratic as the solution is approached.
###############################################################
lnx1% pwd; ls
/home/phys410/nonlin/newt2
Makefile newt2.f
lnx1% make
pgf77 -g -c newt2.f
pgf77 -g -L/usr/local/PGI/lib newt2.o -lp410f -llapack -lblas \
-o newt2
lnx1% newt2
usage: newt2 <x0> <y0> [<tol>]
###############################################################
# Start with initial guess (1.0,1.0) and use default tolerance
###############################################################
lnx1% newt2 1.0 1.0
Iter x y log10(dx) log10(res)
1 -3.2999966453609808E-02 1.4010001006391706E+00 -0.11 0.70
2 3.7660093320946681E-01 2.2207017966697333E+00 -0.19 -0.40
3 2.6508349149835868E-01 1.9187667230922997E+00 -0.64 -0.30
4 2.7416951525985471E-01 1.9092166705387069E+00 -2.03 -1.19
5 2.7423631305849172E-01 1.9092977465351673E+00 -4.13 -3.95
6 2.7423631371214592E-01 1.9092977458408303E+00 -9.17 -8.33
0.2742363137121459 1.909297745840830
###############################################################
# Start with initial guess (10.0,10.0)
###############################################################
lnx1% newt2 10.0 10.0
Iter x y log10(dx) log10(res)
1 1.1551311217431483E+01 8.5653933652294452E+00 0.17 1.43
2 5.2821340061726980E+00 6.2494950887340224E+00 0.67 0.26
3 7.9156169058357619E+00 7.0845635560826592E+00 0.29 0.58
4 8.0553488925966921E+00 7.0945184795080038E+00 -1.00 -0.08
5 8.0478800969985382E+00 7.0913532277563132E+00 -2.24 -1.34
6 8.0480621354266226E+00 7.0914295327798467E+00 -3.86 -2.93
7 8.0480622340064549E+00 7.0914295740731097E+00 -7.12 -6.20
8.048062234006455 7.091429574073110
###############################################################
# Start with initial guess (100.0,100.0)
###############################################################
lnx1% newt2 100.0 100.0
Iter x y log10(dx) log10(res)
1 1.4561314470371519E+02 5.4378394341111459E+01 1.66 3.82
2 1.9021837653952545E+02 3.7701738714769562E+01 1.53 3.17
3 2.0349983567820647E+02 3.5070267397907138E+01 0.98 2.29
4 2.0392234856561166E+02 3.5007684984188501E+01 -0.52 0.70
5 2.0390326095147370E+02 3.5005993323580434E+01 -1.87 -0.53
6 2.0391023928640129E+02 3.5006591323292412E+01 -2.31 -0.59
7 2.0391061250942664E+02 3.5006623302706338E+01 -3.58 -1.92
8 2.0391061457091234E+02 3.5006623479357074E+01 -5.83 -4.18
9 2.0391061457097669E+02 3.5006623479362588E+01 -10.34 -8.68
203.9106145709767 35.00662347936259
###############################################################
# Start with initial guess (0.0,0.0), generates singular
# Jacobian
###############################################################
lnx1% newt2 0.0 0.0
Iter x y log10(dx) log10(res)
newt2: dgesv failed.
###############################################################
# Start with initial guess (1.0,1.0) but use more stringent
# tolerance
###############################################################
lnx1% newt2 1.0 1.0 1.0e-15
Iter x y log10(dx) log10(res)
1 -3.2999966453609808E-02 1.4010001006391706E+00 -0.11 0.70
2 3.7660093320946681E-01 2.2207017966697333E+00 -0.19 -0.40
3 2.6508349149835868E-01 1.9187667230922997E+00 -0.64 -0.30
4 2.7416951525985471E-01 1.9092166705387069E+00 -2.03 -1.19
5 2.7423631305849172E-01 1.9092977465351673E+00 -4.13 -3.95
6 2.7423631371214592E-01 1.9092977458408303E+00 -9.17 -8.33
7 2.7423631371214592E-01 1.9092977458408303E+00 -16.28 -16.07
0.2742363137121459 1.909297745840830