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We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed in the paper. We view a Hilbert space-filling curve as a permutation which maps two-dimensional 2 n 2 n data elements stored in the row major or column major order to the order of traversing a Hilbert space-filling curve. The tensor… (More)

We use a tensor product based multi-linear algebra theory to formulate three-dimensional Hilbert space-filling curves. A 3-D Hilbert space-filling curve is specified as a permutation which rearranges three-dimensional 2 n 2 n 2 n data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of… (More)

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