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Lecture
Newton method for systems: Fixed point iterations
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Newton's Method: Convergence and Applications
Covers the convergence of Newton's method and its applications in numerical analysis.
Newton Method: Data Interpolation
Covers the Newton method for finding zeros of functions using data interpolation.
Fixed Point Theorem: Convergence of Newton's Method
Covers the fixed point theorem and the convergence of Newton's method, emphasizing the importance of function choice and derivative behavior for successful iteration.
Fixed Point Method
Covers the fixed point method for finding x bar = g(x bar) and demonstrates convergence and divergence of sequences.
Bethe Free Entropy
Covers the computation of Bethe free entropy and the interpretation of messages between variables and factors.
Computational Geomechanics: Unconfined Flow Analysis
Explores unconfined flow analysis in geomechanics, emphasizing iterative solution methods and boundary condition considerations.
Fixed Point Methods: Non-linear Equations Solution
Explores fixed point methods for non-linear equations and dynamic models in MATLAB.
Electrical Circuit: Fixed Point Methods
Explores applying fixed point methods to solve electrical circuit equations and find diode voltage.
The Banach Fixed Point Theorem
Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.
Local Inverse Theorems
Covers the local inverse theorem, diffeomorphisms, contraction mappings, and the Jacobian determinant.
