Matrix-matrix multiplication is perhaps the most important operation used as a
basic building block in dense linear algebra. A computer with a hierarchical memory architectures has memory that is organized in layers, with small and fast memories close to the processor, and big and slow memories further away from it.
Classical matrix-matrix multiplication is an operation particularly suited for such architectures, as it exhibits a large degree of data reuse, so expensive data movements can be amortized over a lot of computation. This dissertation advances the theory of
how to optimally reuse data during matrix-matrix multiplication on hierarchical memory architectures, and it uses this understanding to develop new practical algorithms for matrix-matrix multiplication that exhibit improved properties related to data movement.Computer Science
