Cache oblivious matrix operations using peano curves

Abstract

Algorithms are called cache oblivious, if they are designed to benefit from any kind of cache hierarchy - regardless of its size or number of cache levels. In linear algebra computations, block recursive techniques are a common approach that, by construction, lead to inherently local data access patterns, and thus to an overall good cache performance [3]. We present block recursive algorithms that use an element ordering based on a Peano space filling curve to store the matrix elements. We present algorithms for matrix multiplication and LU decomposition, which are able to minimize the number of cache misses on any cache level. © Springer-Verlag Berlin Heidelberg 2007.