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Furthermore, the matrix multiplication can be easily implemented by a convolution layer.
Given the eigendecomposition, the nth power of A (i.e., n-fold iterated matrix multiplication) can be calculated via An = (VDV−1)n = VDV−1VDV−1...VDV−1 = VDnV−1 and the power of a diagonal matrix can be calculated by taking the corresponding powers of the diagonal entries, which is much easier than doing the exponentiation for A instead.
The standard sum-product matrix multiplication can also be replaced by a sum-min matrix multiplication.
Nevertheless, practical fast matrix multiplication can be obtained by using specialized hardware [ 40, 41] (see Section 6).
Since the matrix multiplication can be implemented by performing two r 2 × r 2 matrix multiplications (Equation 1), T (r) is given by T (r ) = 2 D (r ) + 2 M r 2 + Θ (r 2 ).
In the following observation, we point out how matrix multiplication can be computed as a composition of two parts, where each of the items (1-3) in the observation addresses a partitioning in one of the three dimensions.
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The approach is also efficient as sensing matrices with fast matrix multiplication algorithms can be used, in particular in the case of Fourier measurements.
It is also efficient as sensing matrices with fast matrix multiplication algorithms can be used, thus reducing the need in memory requirement and computational power.
On the contrary, it took only 380 s for training D. Because D is a diagonal matrix, simple vector multiplication can be used instead of large matrix multiplication.
GPUs only care about these specific things like matrix multiplication, and you can do it really fast".
However, the polynomial method needs to calculate the high order matrix multiplication, therefore, it can not be implemented easily.
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