Lectures related to Jacobi Method: Part I

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

Matrix Construction and Function Manipulation

Covers tips on matrix construction and function manipulation using MATLAB.

Linear Systems: Iterative Methods

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

Jacobi Method: Part I

Introduces the Jacobi method for solving linear systems by iteratively updating the diagonal elements of a matrix.

Linear Systems: Direct Methods

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Jacobi and Gauss-Seidel methods

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

Numerical Analysis: Linear Systems

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.

Linear Systems: Convergence and Methods

Explores linear systems, convergence, and solving methods with a focus on CPU time and memory requirements.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Iterative Methods for Linear Equations

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

Iterative Methods: Linear Systems

Covers iterative methods for solving linear systems and discusses convergence criteria and spectral radius.

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Nonlinearity: Methods and Examples

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

Iterative Methods for Linear Systems

Covers iterative methods for solving linear systems of equations and discusses the convergence properties of methods like Richardson's method.

Numerics: semester project

Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Iterative Methods: Linear Systems

Covers iterative methods for solving linear systems, emphasizing convergence analysis and well-chosen matrices.

Solving the linear system - Nonlinearity

Explores solving linear systems and addressing nonlinearity in numerical flow simulations using multigrid and linearization methods.

Linear Systems: Stability and Solutions

Explores stability and solutions of linear systems in continuous and discrete time.

Preconditioned Richardson Method

Covers the Preconditioned Richardson Method for solving linear systems and the impact of preconditioning on convergence.

Matrix Exponential: Properties and Convergence

Explores the properties and convergence of the matrix exponential for linear systems.