Concept

Preconditioner

Related lectures (31)

Covers the Preconditioned Richardson Method for solving linear systems and the impact of preconditioning on convergence.

Jacobi and Gauss-Seidel methods

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

Richardson Method: Preconditioned Iterative Solvers

Covers the Richardson method for solving linear systems with preconditioned iterative solvers and introduces the gradient method.

Manopt: Optimization on Manifolds

Introduces Manopt, a toolbox for optimization on manifolds, covering gradient and Hessian checks, solver calls, and manual caching.

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

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

Linear Systems: Richardson's Method

Covers Richardson's method for solving linear equations and its applications in system solutions and error control.

Linear Systems: Iterative Methods

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

Conjugate Gradient Method: Iterative Optimization

Covers the conjugate gradient method, stopping criteria, and convergence properties in iterative optimization.

Conjugate Gradient Method

Covers the Conjugate Gradient method for solving linear systems efficiently.

Conjugate Gradient Methods

Explores gradient and conjugate gradient methods for solving linear systems efficiently.

Regression & Systemed Lineaires

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

Iterative Solvers: Theory and Comparison

Explores solving linear systems iteratively and compares different solvers based on worst-case assumptions and convergence measures.

Conjugate Gradient Methods: Overview

Provides an overview of conjugate gradient methods, including preconditioning, nonlinear conjugate gradient, and singular value decomposition.

Descent methods and line search: Preconditioned steepest descent

Introduces preconditioning in optimization problems and explains steepest descent iteration.

Objective function, Preconditioning

Explores the condition number in optimization and the technique of preconditioning.

Iterative Methods for Linear Equations

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

Construction of an Iterative Method II

Covers the construction of an iterative method for linear systems and introduces relaxation and residual analysis.

Eigenvalues and Eigenvectors

Explores eigenvalues, eigenvectors, and methods for solving linear systems with a focus on rounding errors and preconditioning matrices.

Data Abstraction: Rational Numbers

Covers data abstraction in rational numbers, including client's view, self-reference, preconditions, assertions, constructors, and end markers.