Gauss-Seidel Method

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Solving the linear system - Nonlinearity

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

Iterative Methods: Linear Systems

Explores iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods, Cholesky factorization, and preconditioned conjugate gradient.

Direct and Iterative Methods for Linear Equations

Explores direct and iterative methods for solving linear equations, emphasizing symmetric matrices and computational cost.

Iterative Methods: Error Control and Linear Systems Resolution

Explores iterative methods for solving linear systems with a focus on error control.

Matrix Factorizations: LU Decomposition

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

Matrix Equations: Finding Free Variables

Explains how to find free variables in matrix equations and analyze characteristic polynomials.

Eigenvalues and Eigenvectors: Understanding Matrix Properties

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Jacobi Method: Part I

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

Singular Value Decomposition: Applications and Interpretation

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

Linear Systems: Triangular Matrices

Focuses on transforming linear systems into triangular matrices to simplify the process of finding solutions.