'Gauss seidel method' diaporamas de présentation

Lecture13

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Linear Systems

Linear Systems. Numerical Methods. Jacobi Iterative Method. Iterative methods provide an alternative to the elimination methods. Choose an initial guess (i.e. all zeros) and Iterate until the equality is satisfied. No guarantee for convergence! Each iteration takes O(n 2 ) time!.

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Linear System

Linear System. We want to solve the following linear system. Example: Solve:. 10 -1 2 0 -1 11 -1 3 2 -1 10 -1 0 3 -1 8. Remark:. (1) has a unique solution. A is invertable. Remark:. A is invertable. det(A)=0. Remark:. A is invertable.

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Solving Systems of Linear Equations: Iterative Methods

Solving Systems of Linear Equations: Iterative Methods. Contents. Introduction Basic Idea Jacobi Method Gauss-Seidel Method Successive Over Relaxation (SOR) Summary. Introduction (1/2).

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Multigrid Methods Shijie Zhong Dept. of Physics University of Colorado Boulder, Colorado

Multigrid Methods Shijie Zhong Dept. of Physics University of Colorado Boulder, Colorado Workshop for Advancing Numerical Modeling of Mantle Convection and Lithospheric Dynamics July 2008, UC-Davis. Numerical modeling. A scientific problem ?. Partial differential equations

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Gauss-Siedel Method

Gauss-Siedel Method. Gauss-Seidel Method. An iterative method. Basic Procedure : Algebraically solve each linear equation for x i Assume an initial guess solution array Solve for each x i and repeat

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Chapter 12: Iterative Methods

Chapter 12: Iterative Methods. Uchechukwu Ofoegbu Temple University. Gauss-Seidel Method. The Gauss-Seidel method is the most commonly used iterative method for solving linear algebraic equations [ A ]{ x }={ b }.

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Chapter 12: Iterative Methods

Chapter 12: Iterative Methods. Uchechukwu Ofoegbu Temple University. Gauss-Seidel Method. The Gauss-Seidel method is the most commonly used iterative method for solving linear algebraic equations [ A ]{ x }={ b }.

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Chapter 11

Chapter 11. Special Matrices and Gauss-Seidel Chapter 11. Certain matrices have particular structures that can be exploited to develop efficient solution schemes.

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Chapter 11

Chapter 11. Special Matrices and Gauss-Seidel Chapter 11. Certain matrices have particular structures that can be exploited to develop efficient solution schemes.

372 views • 12 slides

Chapter 11

Chapter 11. Special Matrices and Gauss-Seidel Chapter 11. Certain matrices have particular structures that can be exploited to develop efficient solution schemes.

240 views • 12 slides