Lecture

Jacobi and Gauss-Seidel methods

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Description

This lecture covers the Jacobi and Gauss-Seidel methods for solving linear systems. The Jacobi method assumes diagonal dominance, while the Gauss-Seidel method considers the lower and upper triangular parts of the matrix. The iterative process is explained, along with the convergence criteria and the importance of the preconditioning matrix.

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Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

Algebra: Linear algebra

Related concepts (32)

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.

Jacobi method

In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.

Power iteration

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