Counting arithmetic operation counts is no longer enough. Illustrate this with some performance experiments on a much simpler problem, matrix multiplication (see handouts). This leads us to analyze memory-access efficiency and caches and points the way to restructuring many algorithms.

Outline of the memory hierarchy: CPU, registers, L1/L2 cache, main memory, and presented simple 2-level ideal-cache model that we can analyze to get the basic ideas.

Analyzed cache complexity of simple row-column matrix multiply, showed that it asymptotically gets no benefit from the cache. Presented blocked algorithm, and showed that it achieves optimal Θ(n³/√Z) cache complexity.