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ITERATION METHODS These are methods which compute a sequence of pro-
 

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
3n3 for
Gaussian elimination is too large for most large sys-
tems. With iteration methods, the cost can often be
reduced to something of cost O

n2

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

  

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

 

Collections: Computer Technologies and Information Sciences