A randomized solver for linear systems with exponential convergence

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4110 LNCS, Issue , 2006, Pages 499-507

  Strohmer, Thomas ^a   Vershynin, Roman ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; COMPUTERIZED TOMOGRAPHY; CONVERGENCE OF NUMERICAL METHODS; DIGITAL SIGNAL PROCESSING; ITERATIVE METHODS; RANDOM PROCESSES;

CONJUGATE GRADIENT ALGORITHMS; ITERATIVE ALGORITHMS; KACZMARZ METHOD;

LINEAR SYSTEMS;

EID: 33750060286     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11830924_45     Document Type: Conference Paper

References (17)

1. C. Cenker, H. G. Feichtinger, M. Mayer, H. Steier, and T. Strohmer. New variants of the POCS method using affine subspaces of finite codimension, with applications to irregular sampling. In Proc. SPIE: Visual Communications and Image Processing, pages 299-310, 1992.
2. F. Deutsch. Rate of convergence of the method of alternating projections. In Parametric optimization and approximation (Oberwolfach, 1983), volume 72 of Internat. Schriftenreihe Numer. Math., pages 96-107. Birkhäuser, Basel, 1985.
3. F. Deutsch and H. Hundal. The rate of convergence for the method of alternating projections. II. J. Math. Anal Appl., 205(2):381-405, 1997.
4. A. Edelman. Eigenvalues and condition numbers of random matrices. SIAM J. Matrix Anal. Appl., 9(4):543-560, 1988.
5. A. Frieze, R. Kannan and S. Vempala, Fast Monte-Carlo Algorithms for finding low-rank approximations, Proceedings of the Foundations of Computer Science, 1998, pp. 378-390,
6. journal version in Journal of the ACM 51 (2004), 1025-1041
7. A. Galántai. On the rate of convergence of the alternating projection method in finite dimensional spaces. J. Math. Anal. Appl., 310(1):30-44, 2005.
8. S. Geman. A limit theorem for the norm of random matrices. Ann. Probab., 8(2):252-261, 1980.
9. G.H. Golub and C.F. van Loan. Matrix Computations. Johns Hopkins, Baltimore, third edition, 1996.
10. G.T. Herman. Image reconstruction from projections. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1980. The fundamentals of computerized tomography, Computer Science and Applied Mathematics.
11. G.T. Herman and L.B. Meyer. Algebraic reconstruction techniques can be made computationally efficient. IEEE Transactions on Medical Imaging, 12(3):600-609, 1993.
12. G.N. Hounsfield. Computerized transverse axial scanning (tomography): Part I. description of the system. British J. Radiol, 46:1016-1022, 1973.
13. S. Kaczmarz. Angenäherte Auflösung von Systemen linearer Gleichungen. Bull. Internat. Acad. Polon. Sci. Lettres A, pages 335-357, 1937.
14. F. Natterer. The Mathematics of Computerized Tomography. Wiley, New York, 1986.
15. M. Rudelson and R. Vershynin. Sampling from large matrices: an approach through geometric functional analysis, 2006. preprint.
16. K.M. Sezan and H. Stark. Applications of convex projection theory to image recovery in tomography and related areas. In H. Stark, editor, Image Recovery: Theory and application, pages 415-462. Acad. Press, 1987.
17. A. van der Sluis and H.A. van der Vorst. The rate of convergence of conjugate gradients. Numer. Math., 48:543-560, 1986.