lecture6 - Numerical Methods in Engineering ENGR 391 System...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Numerical Methods in Engineering ENGR 391 Faculty of Engineering and Computer Sciences Concordia University System of linear equations
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Pitfalls of Gauss Elimination Methods Division by zero It is possible that during both elimination and back-substitution phases a division by zero can occur. Here we have a division by zero if we replace in the above formula for Gauss elimination (the same thing will happen if we use a very small number). The pivoting technique has been developed to avoid this problem. ° ¯ ° ® ­ ± ± ± ± ± ± 7 5 1 2 5 1 3 7 8 5 4 0 3 2 1 3 2 1 3 2 1 x x x x x x x x x Numerical problems
Background image of page 2
Pitfalls of Gauss Elimination Methods Round-off errors The large number of equations to be solved induces a propagation of the errors. A rough rule of thumb is that round-off error may be important when dealing with 100 or more equations. Always substitute your answers back into the original equations to check whenever a substantial errors has occurred
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ill-conditioned systems Systems where small changes in coefficients result in large changes in the solution. It happens when two or more equations are nearly identical, resulting a wide ranges of answers to approximately satisfy the equations.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/11/2011 for the course ENGR 391 taught by Professor Hoidick during the Winter '09 term at Concordia Canada.

Page1 / 12

lecture6 - Numerical Methods in Engineering ENGR 391 System...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online