chapter12 - Iterative Methods Silvana Ilie MTH510 Numerical...

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Unformatted text preview: Iterative Methods Silvana Ilie MTH510 Numerical Analysis Department of Mathematics, Ryerson University Iterative Methods p. 1/11 Chapter Objectives Understanding the difference between the Gauss-Seidel and Jacobi methods. Knowing how to assess diagonal dominance and knowing what it means. Recognizing how relaxation can be used to improve convergence of iterative methods. Understanding how to solve systems of nonlinear equations with successive substitution and Newton-Raphson. Iterative Methods p. 2/11 Gauss-Seidel Method The Gauss-Seidel method is the most commonly used iterative method for solving linear algebraic equations [ A ] { x } = { b } . The method solves each equation in a system for a particular variable, and then uses that value in later equations to solve later variables. For a 3 3 system with nonzero elements along the diagonal, for example, the j th iteration values are found from the j- 1 th iteration using: x j 1 = b 1- a 12 x j 1 2- a 13 x j 1 3...
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chapter12 - Iterative Methods Silvana Ilie MTH510 Numerical...

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