If good performance is important, consideration must also be given to the computational kernels of the method and how efficiently they can be executed on the target architecture. In this section we summarize for each method Matrix properties. Not every method will work on every problem type, so knowledge of matrix properties is the main criterion for selecting an iterative method.
Methods differ in the operations that they perform.
However, the fact that one method uses more operations than another is not necessarily a reason for rejecting it. Moreover, it should be noted that for iterative methods applied to sparse systems of equations typically a lower performance is to be expected than for direct solution methods for dense systems. The sparsity of the matrix impedes reuse of data in the processor cache, and the indirect addressing of compressed storage schemes inhibits efficient pipelining of operations. Note that we are not including the original system and we ignore scalar storage. Trivial to parallelize.