Lectures related to Gauss-Seidel Method

Jacobi and Gauss-Seidel methods

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

Matrix Construction and Function Manipulation

Covers tips on matrix construction and function manipulation using MATLAB.

Iterative Methods: Linear Systems

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

Numerical Analysis: Linear Systems

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

Linear Systems: Iterative Methods

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

Linear Systems: Diagonal and Triangular Matrices, LU Factorization

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Linear Systems: LU Factorization with Pivoting

Explains the Gaussian elimination algorithm with pivoting and LU factorization for linear systems.

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.

Numerical Analysis: Direct Methods for Linear Systems

Covers direct methods for solving linear systems in numerical analysis.

Linear Systems Resolution

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

Orthogonal Matrices and Triangular Matrices

Explores properties of orthogonal and triangular matrices with linearly independent columns and their mathematical operations.

Nonlinearity: Methods and Examples

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

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Iterative Methods for Linear Equations

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

Construction of an Iterative Method

Covers the construction of an iterative method for linear systems, emphasizing matrix decomposition and convexity.

Linear Systems: Direct Methods

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

Gauss-Seidel Method

Covers the Gauss-Seidel method for solving linear systems through progressive substitution and iterative processes.

Linear Systems: Choleski Factorisation

Covers the Choleski factorisation method for solving linear systems efficiently.

LU Decomposition: Linear Systems Applications

Covers the LU decomposition method applied to linear systems, presenting the system in two steps.

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.