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Stopping Criteria

An iterative method produces a sequence of vectors converging to the vector satisfying the system . To be effective, a method must decide when to stop. A good stopping criterion should

  1. identify when the error is small enough to stop,
  2. stop if the error is no longer decreasing or decreasing too slowly, and
  3. limit the maximum amount of time spent iterating.

For the user wishing to read as little as possible, the following simple stopping criterion will likely be adequate. The user must supply the quantities , , stop_tol, and preferably also :

Here is the algorithm:

Note that if does not change much from step to step, which occurs near convergence, then need not be recomputed. If is not available, the stopping criterion may be replaced with the generally stricter criterion

In either case, the final error bound is . If an estimate of is available, one may also use the stopping criterion

which guarantees that the relative error in the computed solution is bounded by stop_tol.



Previous: Complex Systems
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Next: Data Structures
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Next Page: More Details about Stopping Criteria