TY - GEN
T1 - On sparse representations of linear operators and the approximation of matrix products
AU - Belabbas, Mohamed Ali
AU - Wolfe, Patrick J.
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
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U2 - 10.1109/CISS.2008.4558532
DO - 10.1109/CISS.2008.4558532
M3 - Conference contribution
AN - SCOPUS:51849109153
SN - 9781424422470
T3 - CISS 2008, The 42nd Annual Conference on Information Sciences and Systems
SP - 258
EP - 263
BT - CISS 2008, The 42nd Annual Conference on Information Sciences and Systems
T2 - CISS 2008, 42nd Annual Conference on Information Sciences and Systems
Y2 - 19 March 2008 through 21 March 2008
ER -