On Diagonally Relaxed Orthogonal Projection Methods
2008 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 30, no 1, 473-504 p.Article in journal (Refereed) Published
We propose and studya block-iterative projection method for solving linear equations and/or inequalities.The method allows diagonal componentwise relaxation in conjunction with orthogonalprojections onto the individual hyperplanes of the system, and isthus called diagonally relaxed orthogonal projections (DROP). Diagonal relaxation hasproven useful in accelerating the initial convergence of simultaneous andblock-iterative projection algorithms, but until now it was available onlyin conjunction with generalized oblique projections in which there isa special relation between the weighting and the oblique projections.DROP has been used by practitioners, and in this papera contribution to its convergence theory is provided. The mathematicalanalysis is complemented by some experiments in image reconstruction fromprojections which illustrate the performance of DROP.
Place, publisher, year, edition, pages
Philadelphia, PA, United States: Society for Industrial and Applied Mathematics, 2008. Vol. 30, no 1, 473-504 p.
block iteration, convex feasibility, diagonal relaxation, projection methods, simultaneous algorithms
IdentifiersURN: urn:nbn:se:liu:diva-13235DOI: 10.1137/050639399ISI: 000208048600006OAI: oai:DiVA.org:liu-13235DiVA: diva2:18093