Abstract
We consider the conjectured O ( N 2 + 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 computation of A ⋅ B to be carried out using the conjectured O ( N 2 + ϵ ) operations. Additionally, in the process of developing our matrix multiplication procedure, we present a modified version of Indyk's recently proposed extractor-based CS algorithm [P. Indyk, Explicit constructions for compressed sensing of sparse signals, in: SODA, 2008] which is resilient to noise.
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