Concept
Iterative method
Related lectures (480)
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Covers Richardson's method for solving linear equations and its applications in system solutions and error control.
Nonlinear Optimization
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Covers Newton's method on Riemannian manifolds, focusing on second-order optimality conditions and quadratic convergence.
Solving Systems of Nonlinear Equations
Covers the Newton-Raphson method, Jacobian matrix, and iterative schemes for solving nonlinear equations.
Linear Systems: Direct and Iterative Methods
Explores linear systems, covering direct and iterative methods for solving them with a focus on round-off errors and Richardson's algorithm.
Iterative Methods: Jacobi
Covers the Jacobi iterative method for solving electrostatic problems and discusses convergence and practical examples.
Kinetic Theory of Plasma: Linearized Vlasov Equations
Explores the kinetic theory of plasma, focusing on linearized Vlasov equations in hot magnetized plasmas and the behavior of plasma particles in phase space.
Differentiability Theorems
Explores differentiability theorems, including partial derivatives, existence of derivatives, and Schwartz's theorem reciprocals.
Transporters: a proxy for parallel transportMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores transporters as a practical alternative to parallel transport, discussing minimal requirements, examples with matrices, pragmatic choices, and optimization algorithms.
Exam Problems: Nonlinear Equations & ODEs
Covers exam-like problems on nonlinear equations, ODEs, and numerical methods.