Applications in Linear Algebra
The Strassen algorithm for matrix multiplication is based on splitting the matrices in four blocks, and then recursively each of these blocks in four smaller blocks, until the blocks are single elements (or more practically: until reaching matrices so small that the trivial algorithm is faster). Arranging the matrix elements in Z-order then improves locality, and has the additional advantage (compared to row- or column-major ordering) that the subroutine for multiplying two blocks does not need to know the total size of the matrix, but only the size of the blocks and their location in memory. Effective use of Strassen multiplication with Z-order has been demonstrated, see Valsalam and Skjellum's 2002 paper.
Read more about this topic: Z-order Curve
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