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MATLAB Function Reference Volume 1: A - E - Bad Request

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icg<br />

2-152<br />

relative residual<br />

10 0<br />

10 −5<br />

10 −10<br />

10<br />

0 1 2 3 4 5 6 7 8<br />

−15<br />

1e−12<br />

1e−14<br />

1e−10<br />

1e−8<br />

1e−6<br />

iteration number<br />

This does not give us any idea of the time involved in creating the incomplete<br />

factors and then computing the solution. The following graph plots the drop<br />

tolerance of the incomplete LU factors against the time to compute the<br />

preconditioner, the time to iterate once the preconditioner has been computed,<br />

and their sum, the total time to solve the problem. The time to produce the<br />

factors does not increase very quickly with the fill-in, but it does slow down the<br />

average time for an iteration. Since fewer iterations are performed, the total<br />

time to solve the problem decreases. west0479 is quite a small matrix, only<br />

139-by-139, and preconditioned bicg still takes longer than backslash.

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