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Block-iterative algorithms with diagonally scaled oblique projections for the linear feasibility problem
Univ Haifa, Dept Math, IL-31905 Haifa, Israel Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Scientific Computing.
2002 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, Vol. 24, no 1, 40-58 p.Article in journal (Refereed) Published
Abstract [en]

We formulate a block- iterative algorithmic scheme for the solution of systems of linear inequalities and/ or equations and analyze its convergence. This study provides as special cases proofs of convergence of ( i) the recently proposed component averaging ( CAV) method of Censor, Gordon, and Gordon [ Parallel Comput., 27 ( 2001), pp. 777 808], ( ii) the recently proposed block- iterative CAV ( BICAV) method of the same authors [ IEEE Trans. Medical Imaging, 20 ( 2001), pp. 1050 1060], and ( iii) the simultaneous algebraic reconstruction technique ( SART) of Andersen and Kak [ Ultrasonic Imaging, 6 ( 1984), pp. 81 94] and generalizes them to linear inequalities. The first two algorithms are projection algorithms which use certain generalized oblique projections and diagonal weighting matrices which reflect the sparsity of the underlying matrix of the linear system. The previously reported experimental acceleration of the initial behavior of CAV and BICAV is thus complemented here by a mathematical study of the convergence of the algorithms.

Place, publisher, year, edition, pages
2002. Vol. 24, no 1, 40-58 p.
Keyword [en]
block-iterative algorithms, component averaging (CAV), block-iterative CAV, simultaneous algebraic reconstruction technique, oblique projections, linear feasibility problem
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-48791OAI: diva2:269687
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-13

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ReferencesLink to record
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