Direct Methods for Linear Equations

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Introduces linear equations, matrices, systems of equations, and solution sets for 2 or 3 unknowns.

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Covers algorithmic complexity and travel time analysis, focusing on measuring the time taken by algorithms and evaluating their performance.

Introduces computational complexity, decision problems, quantum complexity, and probabilistic algorithms, including NP-hard and NP-complete problems.

Explores simplifying belief propagation equations for pairwise models, reducing computational complexity from order n cubed to order n.

Summarizes methods for resolving linear systems, including Gaussian elimination and LU decomposition.

Covers quantifier elimination in Presburger Arithmetic, exposing variables, ensuring coefficients, and handling bounds.

Covers numerical analysis and optimization, focusing on solving linear systems in higher dimensions using finite difference methods.

Explores Projection Pursuit Regression for nonlinear modeling and the trade-offs with interpretability in neural networks.

Covers energy system modelling, optimization, scenarios, predictions, complexities, and controversies in energy models.