Lecture

Iterative Methods: Linear Systems

Related lectures (28)

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.

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Linear Systems: Iterative Methods

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

Linear Systems: Convergence and Methods

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

Linear Systems: Direct Methods

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

Iterative Methods for Linear Equations

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

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.

Jacobi Method: Part I

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

Newton's Method: Convergence and Criteria

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

Numerical Analysis: Linear Systems

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

Iterative Methods: Linear Systems

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

Newton's Method: Convergence Analysis

Explores the convergence analysis of Newton's method for solving nonlinear equations, discussing linear and quadratic convergence properties.

Solving the linear system - Nonlinearity

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

Nonlinearity: Methods and Examples

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

Iterative Methods for Nonlinear Equations

Explores iterative methods for solving nonlinear equations, discussing convergence properties and implementation details.

Computational Geomechanics: Unconfined Flow Analysis

Explores unconfined flow analysis in geomechanics, emphasizing iterative solution methods and boundary condition considerations.

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.

Convergence of Fixed Point Methods

Explores the convergence of fixed point methods and the implications of different convergence rates.

Linear Systems: Factorization and Cholesky

Explores linear systems, Cholesky factorization, LU factorization, and matrix precision.