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

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

Last Time-Matrix Inversion

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

Last Time-Matrix Inversion

Solution

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

Last Time-Matrix Inversion

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

Gauss Seidel

First Iteration: Better Estimate

Gauss Seidel Second Iteration: Better Estimate

Gauss Seidel Iteration Error: Convergence Criterion:

Jacobi Iteration

First Iteration: Better Estimate

Jacobi Iteration Second Iteration: Better Estimate

Jacobi Iteration Iteration Error:

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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