Efficiently Correcting Matrix Products

Efficiently Decodable Error-Correcting List Disjunct Matrices and Applications

A (d, `)-list disjunct matrix is a non-adaptive group testing primitive which, given a set of items with at most d “defectives,” outputs a superset of the defectives containing less than ` non-defective items. The primitive has found many applications as stand alone objects and as building blocks in the construction of other combinatorial objects. This paper studies error-tolerant list disjunct...

Efficiently Evaluating Products of Complex Functions

We present a new technique for importance sampling products of complex functions using wavelets. First, we generalize previous work on wavelet products to higher dimensional spaces and show how this product can be sampled on-thefly without the need of evaluating the full product. This makes it possible to sample products of high-dimensional functions even if the product of the two functions in ...

Evaluating products of matrix pencils and collapsing matrix products

This paper describes three numerical methods to collapse a formal product of p pairs of matrices P = Q p?1 k=0 E ?1 k A k down to the product of a single pair ^ E ?1 ^ A. In the setting of linear relations, the product formally extends to the case in which some of the E k 's are singular and it is impossible to explicitly form P as a single matrix. The methods diier in op count, work space, and...

Parallelizing matrix chain products

The problem of nding an optimal product sequence for sequential multiplication of matrices (the matrix chain ordering problem, MCOP) is well-known and has been studied for a long time. In this paper, we consider the problem of nding an optimal product schedule for evaluating a chain of matrix products on a parallel computer (the matrix chain scheduling problem, MCSP). The diierence between MCSP...

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