3c (i) Splitting or Relaxation Methods Let where is nonsingular. Then . Then the is A=ST, S iterative procedure defined by To be useful requires that is easy to compute. in a reasonable amount of time. Example: Let where is diagonal and and are strictly lower and A=D-L-U, D L U upper triangular, respectively. Then and both are easy to compute, but many iterations are S=D T=L+U: required in practice.
3c (i) Splitting or Relaxation Methods Let A=ST, where S is nonsingular. Then . Then the iterative procedure is defined by To be useful requires that is easy to compute. in a reasonable amount of time. Example: Let A=D-L-U, where D is diagonal and L and U are strictly lower and upper triangular, respectively. Then S=D and T=L+U: both are easy to compute, but many iterations are required in practice.
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