Naïve Gauss Elimination Pitfalls

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Presentation transcript:

Naïve Gauss Elimination Pitfalls http://numericalmethods.eng.usf.edu

Pitfall#1. Division by zero

Is division by zero an issue here?

Is division by zero an issue here? YES Division by zero is a possibility at any step of forward elimination

Pitfall#2. Large Round-off Errors Exact Solution

Solve it on a computer using 6 significant digits with chopping Pitfall#2. Large Round-off Errors Solve it on a computer using 6 significant digits with chopping

Pitfall#2. Large Round-off Errors Solve it on a computer using 5 significant digits with chopping Is there a way to reduce the round off error?

Avoiding Pitfalls Increase the number of significant digits Decreases round-off error Does not avoid division by zero

Avoiding Pitfalls Gaussian Elimination with Partial Pivoting Avoids division by zero Reduces round off error

THE END http://numericalmethods.eng.usf.edu