26-Mar-2024 18:28:48

zero_muller_test():
  MATLAB/Octave version 9.14.0.2306882 (R2023a) Update 4
  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.
26-Mar-2024 18:28:48