What are the advantages of iterative methods of solution of linear equations? When do we use iterative methods?

Following are the advantages of iterative methods over direct methods:
  • Each cycle is O(N2) operations for full storage mode.
  • Round off errors only occurs during O(N2) operations which accure in O(N3) in direct method. 
  • Since each cycle only produces an approximation for the next cycle, an error in a guess will be handled by the next cyle.
  • We can consider round off error to accrue only during the last iterations. 
when to use iterative methods?
  1. When very large matrices are there since they reduce the round off problems. 
  2. Sparse but not bounded matrices since they can reduce computational efforet not oprationg on zeros.
  3. Very large sparse banded matrices due to effeciency. 


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