Independent Python reference checks
===================================
These are not executions of the MATLAB files. Numerical translations check
algorithm logic and example mathematics; MATLAB graphics remain unexecuted.

Quadratic GD: updates=20, f=-8.28571429, gradient_inf=1.49e-08, Gradient tolerance
Quadratic BFGS: updates=8, f=-8.28571429, gradient_inf=1.353e-08, Gradient tolerance
Rosenbrock GD: updates=2000, f=0.000129275308, gradient_inf=0.01432, Iteration limit
Rosenbrock BFGS: updates=34, f=2.745653e-17, gradient_inf=7.702e-08, Gradient tolerance
Bisection sqrt example: 27 midpoint evaluations; x=3.9999999851; interval error bound verified at every step.
All three stationary-point exercise formulas and Cobb-Douglas FOCs/Hessian independently verified.
Non-finite line-search trial is rejected; backtracking reaches the valid minimum.
Bracketing: 41 updates; x=3.83795929; endpoint-value bookkeeping and maximum verified.
Root geometry histories: Newton 6 updates; secant 8 updates; residuals below 1e-10.
Broyden: x=[2. 1.], updates=11, residual=2.21e-12.
Inverse Broyden: x=[2. 1.], updates=11, residual=2.21e-12.
