25 March 2024   9:47:31.868 PM
 
zero_muller_test():
  FORTRAN90 version
  Test zero_muller(), which uses Muller's method,
  with complex arithmeic, to solve a nonlinear equation.
 
test01():
  Demonstrate zero_muller() on F(X) = X*X+9.
 
 
zero_muller():
  Muller's root-finding method (complex root version)
 
 
  Iteration     x_real              x_imag             ||fx||           ||disc||
 
    -2        0.5000000000        0.5000000000        9.0138781887
    -1        0.0000000000        1.0000000000        8.0000000000
     0        1.0000000000        0.0000000000       10.0000000000
     1        0.0000000000       -3.0000000000        0.0000000000       18.0000000000
 
zero_muller():
  Absolute convergence of |F(X)|.
 
     X   =         0.0000000000       -3.0000000000
 
  with function value F(X):
 
    FX   =         0.0000000000        0.0000000000
  ||FX|| =         0.0000000000
 
test02():
  Demonstrate zero_muller() on F(X) = (X*X+4)*(X-10)*(X+20).
 
 
zero_muller():
  Muller's root-finding method (complex root version)
 
 
  Iteration     x_real              x_imag             ||fx||           ||disc||
 
    -2        0.5000000000        0.5000000000      786.3827391926
    -1        0.0000000000        1.0000000000      603.7458074389
     0        1.0000000000        0.0000000000      945.0000000000
     1        0.0242802733        2.0507061379       46.6853784403   292576.8813244862
     2       -0.0016499786        1.9990380412        1.5656742803  7255213.6000903565
     3       -0.0000011428        2.0000011261        0.0013154356     2477.9662226890
     4        0.0000000000        2.0000000000        0.0000000022        0.0000258907
 
zero_muller():
  Absolute convergence of the X increment.
 
 
     X   =         0.0000000000        2.0000000000
 
  with function value F(X):
 
    FX   =        -0.0000000000       -0.0000000022
  ||FX|| =         0.0000000022
 
test03():
  Demonstrate zero_muller() on Zhelyazkov's function.
 
 
zero_muller():
  Muller's root-finding method (complex root version)
 
 
  Iteration     x_real              x_imag             ||fx||           ||disc||
 
    -2        0.5000000000        0.5000000000        1.7780343017
    -1        0.0000000000        1.0000000000        2.7212864609
     0        1.0000000000        0.0000000000        1.1398341819
     1        1.5705799215       -0.0000004486        0.0000012222        3.6964136697
     2        1.5705798926        0.0000000000        0.0000000000       16.6875551235
 
zero_muller():
  Absolute convergence of |F(X)|.
 
 
     X   =         1.5705798926        0.0000000000
 
  with function value F(X):
 
    FX   =        -0.0000000000        0.0000000000
  ||FX|| =         0.0000000000
 
 
zero_muller():
  Muller's root-finding method (complex root version)
 
 
  Iteration     x_real              x_imag             ||fx||           ||disc||
 
    -2       -1.0000000000        2.0000000000        8.4140172656
    -1        1.0000000000        2.0000000000        6.7016733534
     0        0.0000000000        1.0000000000        2.7212864609
     1       -0.5802520858       -0.0000000937        0.0000002667      118.2853729480
     2       -0.5802520567       -0.0000000000        0.0000000000      128.4099686054
 
zero_muller():
  Absolute convergence of the X increment.
 
 
     X   =        -0.5802520567       -0.0000000000
 
  with function value F(X):
 
    FX   =        -0.0000000000        0.0000000000
  ||FX|| =         0.0000000000
 
zero_muller_test():
  Normal end of execution.

25 March 2024   9:47:31.869 PM