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Na

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Title: Gaussian Elimination Subject: Simultaneous Linear Equations Author: Autar Kaw Keywords: Power Point, Gaussian Elimination, Simultaneous Linear Equations – PowerPoint PPT presentation

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Title: Na


1
Naïve Gauss EliminationPitfalls
http//numericalmethods.eng.usf.edu
2
Pitfall1. Division by zero
3
Is division by zero an issue here?
4
Is division by zero an issue here? YES
Division by zero is a possibility at any step of
forward elimination
5
Pitfall2. Large Round-off Errors
Exact Solution
6
Pitfall2. Large Round-off Errors
Solve it on a computer using 6 significant digits
with chopping
7
Pitfall2. 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?
8
Avoiding Pitfalls
  • Increase the number of significant digits
  • Decreases round-off error
  • Does not avoid division by zero

9
Avoiding Pitfalls
  • Gaussian Elimination with Partial Pivoting
  • Avoids division by zero
  • Reduces round off error

10
  • THE END
  • http//numericalmethods.eng.usf.edu
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