Structural conditions for projection-cost preservation via randomized matrix multiplication

Coreset Construction via Randomized Matrix Multiplication

Coresets are small sets of points that approximate the properties of a larger point-set. For example, given a compact set S ⊆ R, a coreset could be defined as a (weighted) subset of S that approximates the sum of squared distances from S to every linear subspace of R. As such, coresets can be used as a proxy to the full dataset and provide an important technique to speed up algorithms for solvi...

Matrix-Vector Multiplication via Erasure Decoding

The problem of fast evaluation of a matrix-vector product over GF (2) is considered. The problem is reduced to erasure decoding of a linear error-correcting code. A large set of redundant parity check equations for this code is generated. The multiplication algorithm is derived by tracking the execution of the message-passing algorithm on the obtained set of parity check equations. The obtained...

All Pairs Shortest Paths via Matrix Multiplication

A Bootstrap Method for Error Estimation in Randomized Matrix Multiplication

In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension reduction, which accelerates computations, but also creates random approximation error. In this way, the dimension reduction step encodes a tradeoff between cost an...

Analysis of a randomized approximation scheme for matrix multiplication

This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by [Sar06] based on a random rotation followed by uniform column sampling. The result follows from a matrix version of Bernstein’s inequality and a tail inequality for quadratic forms in subgaussian random vectors.