Summary: ITERATION METHODS
These are methods which compute a sequence of pro-
gressively accurate iterates to approximate the solu-
tion of Ax = b.
We need such methods for solving many large lin-
ear systems. Sometimes the matrix is too large to
be stored in the computer memory, making a direct
method too difficult to use.
More importantly, the operations cost of 2
Gaussian elimination is too large for most large sys-
tems. With iteration methods, the cost can often be
reduced to something of cost O
or less. Even
when a special form for A can be used to reduce the
cost of elimination, iteration will often be faster.
There are other, more subtle, reasons, which we do