Lectures related to Resolution Sequence: Defining a Procedure

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Analysis of Trust Regions with Cauchy Steps

Explores the analysis of trust regions with Cauchy steps in optimization.

Solving Equations: Newton's Method

Covers Newton's method conditions and convergence, extension to multiple variables, and linear models.

Nonlinear Equations: Convergence and Taylor Polynomials

Explores nonlinear equations, emphasizing convergence and Taylor polynomials for function approximation.

Nonlinear Equations: Fixed Point Method

Covers the topic of nonlinear equations and the fixed point method.

Descent methods and line search: Finiteness of the line search algorithm

Explores the Wolfe conditions for line search algorithms and proves the finiteness of the line search parameter.

Newton's Method: Convergence and Criteria

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

Iterative Methods for Linear Equations

Covers iterative methods for solving linear equations and analyzing convergence, including error control and positive definite matrices.

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.

Limits of Recursive Sequences

Explores limits of recursive sequences, convergence, boundedness, and algebraic operations related to limits at infinity.

Jacobi and Gauss-Seidel methods

Explains the Jacobi and Gauss-Seidel methods for solving linear systems iteratively.

Fixed Point Method

Covers the fixed point method for convergence and linear error reduction.

Energy Conversion Methods

Covers energy system, numerical methods, Newton-Raphson, convergence, and efficient equation solving.

Optimisation in Energy Systems

Explores optimization in energy system modeling, covering decision variables, objective functions, and different strategies with their pros and cons.

Link-Based Ranking: HITS

Covers the HITS algorithm, computing hubs and authorities, convergence, and sample results.

Root Finding Methods: Secant and Newton's Methods

Covers numerical methods for root finding, focusing on the secant and Newton's methods.

Degree of Freedom Analysis

Explores degree of freedom analysis, redundancy, and data reconciliation in process modeling and optimization.

Convergence Analysis: Iterative Methods

Covers the convergence analysis of iterative methods and the conditions for convergence.

Solving Equations with Newton's Method

Introduces Newton's method for solving non-linear equations iteratively, highlighting its fast convergence but also its potential failure to converge in some cases.