Derivatives, Gradients, Jacobians and Hessians
7 days ago
- #calculus
- #mathematics
- #optimization
- Derivatives are fundamental in calculus, indicating how a function changes at each point.
- Derivatives are used for optimization, such as finding minima or maxima on a graph.
- Gradient descent is an iterative optimization method inspired by derivatives, adjusting step size to find minima.
- Gradients extend derivatives to higher-dimensional functions, providing vectors that indicate the steepest ascent or descent.
- The Jacobian matrix combines gradients of functions with multiple outputs, describing how space is warped at a point.
- The Hessian matrix consists of second derivatives, useful for understanding the curvature of functions in optimization.
- Hessian matrices are computationally intensive but valuable in optimization, with quasi-Newton methods offering alternatives.