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We consider the conjectured O(N2+ϵ) time complexity of multiplying any two N×N matrices A and B. Our main result is a deterministic Compressed Sensing (CS) algorithm that both rapidly and accurately computes A⋅B provided that the resulting matrix product is sparse/compressible. As a consequence of our main result we increase the class of matrices A, for any given N×N matrix B, which allows the exact...
This paper improves on the best-known runtime and measurement bounds for a recently proposed Deterministic sublinear-time Sparse Fourier Transform algorithm (hereafter called DSFT). In (Iwen, 2008 ), (Iwen, 2007), it is shown that DSFT can exactly reconstruct the Fourier transform (FT) of an N-bandwidth signal f, consisting of B Lt N non-zero frequencies, using O(B2ldrpolylog(N)) time and O(B2 ldr...
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