ES240_Chpt12 - ES 240: Scientific and Engineering...

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ES 240: Scientific and Engineering Computation. Iterative Methods and Eigenvalues Chapter 12: Iterative Methods Uchechukwu Ofoegbu Temple University
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ES 240: Scientific and Engineering Computation. Iterative Methods and Eigenvalues Gauss Gauss -Seidel Method 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 3x3 system with nonzero elements along the diagonal, for example, the j th iteration values are found from the j -1 th iteration using: x 1 j = b 1 a 12 x 2 j 1 a 13 x 3 j 1 a 11 x 2 j = b 2 a 21 x 1 j a 23 x 3 j 1 a 22 x 3 j = b 3 a 31 x 1 j a 32 x 2 j a 33
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ES 240: Scientific and Engineering Computation. Iterative Methods and Eigenvalues Gauss Gauss -Seidel Method 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 3x3 system with nonzero elements along the diagonal, for example, the j th
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ES240_Chpt12 - ES 240: Scientific and Engineering...

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