28 March 2024 06:16:53 PM

zero_muller_test():
  C version
  Test zero_muller(), which uses Muller's method,
  with complex arithmetic, 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        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

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        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

zero_muller():
  Muller's root-finding method (complex root version)

  Iteration     x_real              x_imag             ||fx||           ||disc||

    -2       -1.0000000000        2.0000000000        7.2111025509
    -1        1.0000000000        2.0000000000        7.2111025509
     0        0.0000000000        1.0000000000        8.0000000000
     1        0.0000000000       -3.0000000000        0.0000000000      576.0000000000

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

zero_muller_test():
  Normal end of execution.

28 March 2024 06:16:53 PM