Fast Multiplication of Matrices with Decay. (arXiv:1011.3534v1 [cs.DS])

Fast Multiplication of Matrices with Decay. (arXiv:1011.3534v1 [cs.DS]): "

A fast algorithm for the approximate multiplication of matrices with decay is
introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity
in the product space, a different approach from current methods that economize
within the matrix space through truncation or rank reduction. Matrix truncation
(element dropping) is compared to SpAMM for quantum chemical matrices with
approximate exponential and algebraic decay. For matched errors in the
electronic total energy, SpAMM is found to require fewer to far fewer floating
point operations relative to dropping. The challenges and opportunities
afforded by this new approach are discussed, including the potential for high
performance implementations.

"