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Original Articles

Automatic generation of fast algorithms for matrix–vector multiplication

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Pages 626-644 | Received 28 Jun 2015, Accepted 03 Sep 2016, Published online: 16 Mar 2017
 

ABSTRACT

This paper describes the methods for finding fast algorithms for computing matrix–vector products including the procedures based on the block-structured matrices. The proposed methods involve an analysis of the structural properties of matrices. The presented approaches are based on the well-known optimization techniques: the simulated annealing and the hill-climbing algorithm along with its several extensions. The main idea of the proposed methods consists in finding a decomposition of the original matrix into a sparse matrix and a matrix corresponding to an appropriate block-structured pattern. The main criterion for optimizing is a reduction of the computational cost. The methods presented in this paper can be successfully implemented in many digital signal processing tasks.

2010 AMS SUBJECT CLASSIFICATIONS:

Disclosure statement

No potential conflict of interest was reported by the authors.

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