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.
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References
Bader, M., Zenger, C.: Cache oblivious matrix multiplication using an element ordering based on a Peano curve. Linear Algebra and its Applications 417(2-3) (2006)
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Bader, M., Mayer, C. (2007). Cache Oblivious Matrix Operations Using Peano Curves. In: Kågström, B., Elmroth, E., Dongarra, J., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2006. Lecture Notes in Computer Science, vol 4699. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75755-9_64
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DOI: https://doi.org/10.1007/978-3-540-75755-9_64
Publisher Name: Springer, Berlin, Heidelberg
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