Chemical Engineering Hand Written_Notes_Part_44

Chemical Engineering Hand Written_Notes_Part_44 - 90 3....

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90 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES and the Guassian elimination yields (5.9) " 11 00 . 9999 #" x 1 x 2 # = " 2 0 . 9998 # and again due to three digit round o f in our computer, the solution becomes h x 1 x 2 i T = h 11 i Thus, A is a well conditioned numerically only thing that can cause calculation blunders is wrong pivoting strategy. If maximum pivoting is used then natural resistance to round o f the errors is no longer compromised. Now, in order to understand di culties with ill conditioned systems, con- sider another system ( System-2 ) (5.10) " 11 11 . 0001 #" x 1 x 2 # = " 2 2 # By Guassian elimination (5.11) " 11 00 . 0001 #" x 1 x 2 # = " 2 0 # = " x 1 x 2 # = " 2 0 # If we change R.H.S. of the system 2 by a small amount (5.12) " 11 11 . 0001 #" x 1 x 2 # = " 2 2 . 0001 # (5.13) " 11 00 . 0001 #" x 1 x 2 # = " 2 0 . 0001 # = " x 1 x 2 # = " 1 1 # Note that change in the f fth digit of second element of vector b was ampli f ed to change in the f rst digit of the solution. Thus, matrix A in the system 2 is ill conditioned as it is near singular.
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This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

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Chemical Engineering Hand Written_Notes_Part_44 - 90 3....

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