On sparse representations of linear operators and the approximation of matrix products

Details On sparse representations of linear operators and the approximation of matrix products On sparse representations of linear operators and the approximation of matrix products

2007-07-30

arxiv.org/abs/0707.4448v2

Computer Science

Data Structures and Algorithms

6 pages, 3 figures; presented at the 42nd Annual Conference on Information Sciences and Systems (CISS 2008)

Scientific paper

10.1109/CISS.2008.4558532

Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under consideration is sparse is used to decrease the number of necessary measurements while controlling the approximation error. In this paper, we instead focus on applications in numerical analysis, by way of sparse representations of linear operators with the objective of minimizing the number of operations needed to perform basic operations (here, multiplication) on these operators. We represent a linear operator by a sum of rank-one operators, and show how a sparse representation that guarantees a low approximation error for the product can be obtained from analyzing an induced quadratic form. This construction in turn yields new algorithms for computing approximate matrix products.

Affiliated with

Also associated with

No associations

Rating

On sparse representations of linear operators and the approximation of matrix products does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On sparse representations of linear operators and the approximation of matrix products, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On sparse representations of linear operators and the approximation of matrix products will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-360095