The Conjugate Gradients Method (CG)

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Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Covers iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods.

Explores nonlinearity in numerical flow simulation, covering linearization methods and practical examples.

Explores matrix-based and matrix-free approaches for computing the Newton step in optimization on manifolds.

Explores linear systems and iterative methods like gradient descent and conjugate gradient for efficient solutions.

Explores gradient descent with memory, momentum methods, conjugate gradients, and nonlinear CG on manifolds.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers the principles of regression and linear systems, focusing on iterative methods.