Lectures related to Direct and Iterative Methods for Linear Equations

Iterative Methods for Linear Equations

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

Eigenvalues and Optimization: Numerical Analysis Techniques

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

Iterative Methods for Linear Equations

Introduces iterative methods for solving linear equations and discusses the gradient method for minimizing errors.

Numerical Analysis: Linear Systems

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

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Jacobi and Gauss-Seidel methods

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

Iterative Methods for Linear Equations

Explores iterative methods for linear equations, including Jacobi and Gauss-Seidel methods, convergence criteria, and the conjugate gradient method.

Calcul de valeurs propres

Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.

Newton's Method: Convergence and Criteria

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

Direct Methods for Solving Linear Equations

Explores direct methods for solving linear equations and the impact of errors on solutions and matrix properties.

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.

Regression & Systemed Lineaires

Covers the principles of regression and linear systems, focusing on iterative methods.

Symmetric Matrices: Diagonalization

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Effect of Rounding Errors in Linear Systems

Explores the effect of rounding errors in solving linear systems using the LU factorization method.

Diagonalization Techniques: Jacobi Method

Explores the Jacobi method and diagonalization techniques, including similarity transformation, power methods, and QR decomposition.

Iterative Methods for Linear Equations

Introduces iterative methods for linear equations, convergence criteria, gradient of quadratic forms, and classical force fields in complex atomistic systems.

Linear Systems: Iterative Methods

Explores linear systems and iterative methods like gradient descent and conjugate gradient for efficient solutions.

Linear Algebra Basics: Vector Spaces, Transformations, Eigenvalues

Covers fundamental linear algebra concepts like vector spaces and eigenvalues.

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.