Automatic generation of fast algorithms for matrix–vector multiplication

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.

KEYWORDS:

• Fast algorithms
• matrix–vector multiplication
• computational complexity reduction
• block matrices
• simulated annealing
• hill-climbing

2010 AMS SUBJECT CLASSIFICATIONS:

• 15B99
• 68Q10
• 68Q25
• 68W20

Disclosure statement

No potential conflict of interest was reported by the authors.