Optimal selections of stepsizes and blocks for the block-iterative ART

ABSTRACT

The algebraic reconstruction technique (ART) and its generalization the block-iterative ART are often used to solve large scale linear systems Ax=b which arise in many applications, such as image processing. Two ingredients, i.e. stepsizes and blocks, play a key role in block-iterative ART. In this paper we address the problem of how to choose stepsizes and blocks of A so as to achieve optimal convergence rate of the block-iterative ART. We introduce a random cyclic selection method for selecting blocks for the block-iterative ART in order to reduce computational complexity. Our numerical experiments demonstrate the efficiency of our selections of stepsizes and blocks in the block-iterative ART.

COMMUNICATED BY:

• J.-C. Yao

Keywords:

• System of linear equations
• block-iterative ART
• projection
• optimal step size
• optimal blocks
• random selection

2010 Mathematics Subject Classifications:

• 47J20
• 90C25
• 90C30
• 90C52

Acknowledgments

The authors were indebted to the anonymous referees for their critical comments and invaluable suggestions which improved the presentation of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the scientific research project of Tianjin Municipal Education Commission (No. 2018KJ253).