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.

Nonlinearity: Methods and Examples

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

Jacobi Method: Convergence Conditions

Explores the Jacobi method for linear systems, emphasizing convergence conditions 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.

Jacobi Method: Part I

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

Gauss-Seidel Method

Covers the Gauss-Seidel method for solving linear systems with triangular matrices and progressive substitution.

Jacobi Method: Part I

Introduces the Jacobi method for solving linear systems and determining convergence.

Iterative Methods: Error Control and Linear Systems Resolution

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

The Conjugate Gradients Method (CG)

Covers the Conjugate Gradients method for solving linear systems iteratively with quadratic convergence and emphasizes the importance of linear independence among conjugate directions.