Lectures related to Linear Systems: Factorization and Cholesky

Linear Systems: Direct Methods

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

Singular Value Decomposition: Applications and Interpretation

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

Cholesky Factorization: Theory and Algorithm

Explores the Cholesky factorization method for symmetric positive definite matrices.

Linear Systems: Diagonal and Triangular Matrices, LU Factorization

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

Construction of an Iterative Method

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

Construction of an Iterative Method

Covers the construction of an iterative method for linear systems by decomposing a matrix A into P, T, and P_A.

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.

Linear Systems: Convergence and Methods

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

Iterative Methods: Linear Systems

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

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.

Least Squares Solutions

Explains the concept of least squares solutions and their application in finding the closest solution to a system of equations.

QR Factorization: Least Squares System Resolution

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

Numerical Analysis: Direct Methods for Linear Systems

Covers direct methods for solving linear systems in numerical analysis.

Matrix Factorization: LU Decomposition

Explores LU decomposition for matrix factorization and solving linear systems.

Factorisation LU

Explains Gaussian elimination and LU factorization for solving linear systems of equations.

Characterization of Invertible Matrices

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

LU Decomposition: Linear Systems Applications

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

Linear Algebra Review

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Matrix Factorizations: LU Decomposition

Introduces LU decomposition for efficient linear equation solving using matrix factorization.

Linear Systems: LU Factorization with Pivoting

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