Gradient Descent Visualization

Gradient descent is an optimization algorithm used to minimize a function by iteratively moving in the direction of steepest descent. It's widely used in machine learning for training models and finding optimal parameters. This visualization demonstrates how the algorithm converges towards a local minimum by iteratively updating the input based on the gradient of the function:

f(x) = x⁴ - 5x³ + 7x² - 3x

This function, which is a fourth-degree polynomial, exhibits multiple turning points and provides a clear visual representation of how gradient descent behaves in the presence of local minima and maxima.

Try These Examples:

Small alpha (0.01) with initial x = 1.1: Shows slow but stable convergence
Large alpha (0.2) with initial x = 1.5: Oscillate and diverge
Very large alpha (0.3) with initial x = 1.1: Overshoot the global minimum
Optimal alpha (0.1) with initial x = 1.1: Efficient convergence to minimum