Is Linpack the most efficient way to solve systems of equations?
Linpack is not the most efficient software for solving matrix problems. This is mainly due to the way the algorithm and resulting software accesses memory. The memory access patterns of the algorithm has disregard for the multi-layered memory hierarchies of RISC architecture and vector computers, thereby spending too much time moving data instead of doing useful floating-point operations. LAPACK addresses this problem by reorganizing the algorithms to use block matrix operations, such as matrix multiplication in the innermost loops. For each computer architecture block operations can be optimized to account for memory hierarchies, providing a transportable way to achieve high efficiency on diverse modern machines. We use the term Transportable instead of portable because, for fastest possible performance, LAPACK requires that highly optimized block matrix operations be already implemented on each machine. These operations are performed by the Level 3 BLAS in most cases.
