10-Oct-2020 18:46:14 test_nonlin_test MATLAB/Octave version 4.2.2 test_nonlin() defines a set of sample systems of nonlinear equations. test_nonlin_test01 Print the title of each problem. 1 "Generalized Rosenbrock function" 2 "Powell singular function" 3 "Powell badly scaled function" 4 "Wood function" 5 "Helical valley function" 6 "Watson function" 7 "Chebyquad function" 8 "Brown almost linear function" 9 "Discrete boundary value function" 10 "Discrete integral equation function" 11 "Trigonometric function" 12 "Variably dimensioned function" 13 "Broyden tridiagonal function" 14 "Broyden banded function" 15 "Hammarling 2 by 2 matrix square root problem" 16 "Hammarling 3 by 3 matrix square root problem" 17 "Dennis and Schnabel 2 by 2 example" 18 "Sample problem 18" 19 "Sample problem 19" 20 "Scalar problem f(x) = x * ( x - 5 ) * ( x - 5 )" 21 "Freudenstein-Roth function" 22 "Boggs function" 23 "Chandrasekhar function" test_nonlin_test02 Evaluate the norm of the function at the starting point and at the root, if known. # ------------------------------------------Title N ||F(start)|| ||F(root)|| 1 Generalized Rosenbrock function 10 4.91935 0 2 Powell singular function 4 14.6629 0 3 Powell badly scaled function 2 1.06549 3.81479e-07 4 Wood function 4 8550.56 0 5 Helical valley function 3 50 0 6 Watson function 10 94.9722 ? 7 Chebyquad function 9 0.16995 2.31467e-10 8 Brown almost linear function 10 16.5302 0 9 Discrete boundary value function 10 0.0280806 ? 10 Discrete integral equation function 10 0.251827 ? 11 Trigonometric function 10 0.0841175 ? 12 Variably dimensioned function 10 2.24021e+06 0 13 Broyden tridiagonal function 10 4.58258 ? 14 Broyden banded function 10 18.9737 ? 15 Hammarling 2 by 2 matrix square root problem 4 1.73194 0 16 Hammarling 3 by 3 matrix square root problem 9 1.99985 0 17 Dennis and Schnabel 2 by 2 example 2 17.2627 0 18 Sample problem 18 2 2.19511 0 19 Sample problem 19 2 76.3675 0 20 Scalar problem f(x) = x * ( x - 5 ) * ( x - 5 ) 1 16 0 21 Freudenstein-Roth function 2 20.0125 0 22 Boggs function 2 2 6.12323e-17 23 Chandrasekhar function 10 1.02037 ? test_nonlin_test03 Seek a root using fsolve() # ------------------------------------------Title N ||F(start)|| ||F(root)|| 1 Generalized Rosenbrock function 10 4.91935 1.98093 2 Powell singular function 4 14.6629 7.308e-14 3 Powell badly scaled function 2 1.06549 0.00236243 4 Wood function 4 8550.56 4.72484e-07 5 Helical valley function 3 50 8.46601e-08 6 Watson function 10 94.9722 8.18536e-06 7 Chebyquad function 9 0.16995 4.78651e-07 8 Brown almost linear function 10 16.5302 1.74975e-06 9 Discrete boundary value function 10 0.0280806 3.10992e-08 10 Discrete integral equation function 10 0.251827 3.72516e-07 11 Trigonometric function 10 0.0841175 4.54304e-08 12 Variably dimensioned function 10 2.24021e+06 0.000124995 13 Broyden tridiagonal function 10 4.58258 2.86965e-07 14 Broyden banded function 10 18.9737 1.0627e-06 15 Hammarling 2 by 2 matrix square root problem 4 1.73194 0.00200621 16 Hammarling 3 by 3 matrix square root problem 9 1.99985 0.00124138 17 Dennis and Schnabel 2 by 2 example 2 17.2627 2.80587e-07 18 Sample problem 18 2 2.19511 1.87959e-08 19 Sample problem 19 2 76.3675 6.87136e-11 20 Scalar problem f(x) = x * ( x - 5 ) * ( x - 5 ) 1 16 0 21 Freudenstein-Roth function 2 20.0125 6.99888 22 Boggs function 2 2 1.16212e-07 23 Chandrasekhar function 10 1.02037 1.646e-06 test_nonlin_test Normal end of execution. 10-Oct-2020 18:46:17