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ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 19 Solution of Linear System of Equations - Iterative Methods

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Last Time-Matrix Inversion

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[A][A] -1 [A] [A] -1 =[I] If [A] -1 does not exist [A] is singular

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Last Time-Matrix Inversion

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Solution

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Last Time-Matrix Inversion [A] [A] -1 =[I]

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Last Time-Matrix Inversion

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Iterative Methods Recall Techniques for Root finding of Single Equations Initial Guess New Estimate Error Calculation Repeat until Convergence

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Gauss Seidel

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First Iteration: Better Estimate

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Gauss Seidel Second Iteration: Better Estimate

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Gauss Seidel Iteration Error: Convergence Criterion:

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Jacobi Iteration

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First Iteration: Better Estimate

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Jacobi Iteration Second Iteration: Better Estimate

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Jacobi Iteration Iteration Error:

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Homework 11.7 – Use MathCAD to implement Gauss Seidel Iterations 12.14 – Use EXCEL to calculate Inverse Matrix and Solve Equations

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