Fast Distance Multiplication of Unit-Monge Matrices

Fast Multiplication of Matrices with Decay

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 approxi...

Fast multiplication of integer matrices Withdrawn paper

Erratum. Eric Schost discovered a bug in this paper: by construction, formula (7) does not hold, since the matrix Va,n is not invertible whenever l> 2. Unfortunately, we do not see how to repair this bug: not only Va,n is not invertible, but the rank of Va,n is actually very small (and equal to max {q1, , ql}). This makes the proof collapse. We have also tried a few other things, such as fixing...

Fast Multiplication of Interval Matrices (Interval Version of Strassen's Algorithm)

Caching-Efficient Multithreaded Fast Multiplication of Sparse Matrices

Several fast sequential algorithms have been proposed in the past to multiply sparse matrices. These algorithms do not explicitly address the impact of caching on performance. We show that a rather simple sequential cache–efficient algorithm provides significantly better performance than existing algorithms for sparse matrix multiplication. We then describe a multithreaded implementation of thi...

E-Clean Matrices and Unit-Regular Matrices

Let $a, b, k,in K$ and $u, v in U(K)$. We show for any idempotent $ein K$, $(a 0|b 0)$ is e-clean iff $(a 0|u(vb + ka) 0)$ is e-clean and if $(a 0|b 0)$ is 0-clean, $(ua 0|u(vb + ka) 0)$ is too.