Smooth scheme

Related lectures (31)

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Covers smooth sets and functions on manifolds, with a focus on constructing an atlas for a circle.

Covers faster gradient descent methods and projected gradient descent for constrained optimization in machine learning.

Introduces retractions and vector fields on manifolds, providing examples and discussing smoothness and extension properties.

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

Covers the concept of local frames, their construction, and limitations.

Covers Newton's method on Riemannian manifolds, focusing on second-order optimality conditions and quadratic convergence.

Explores Taylor expansions and retractions on Riemannian manifolds, emphasizing second-order approximations and covariant derivatives.

Explores linear response in dynamical systems, emphasizing fractional derivatives and expanding unimodal maps.

Covers coordinate descent, a method for optimizing functions by updating one coordinate at a time.