Matrix probing and its conditioning

SIAM Journal on Numerical Analysis

Volumn 50, Issue 1, 2012, Pages 171-193

  Chiu, Jiawei ^a   Demanet, Laurent ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Conditioning; Large deviation estimates; Preconditioners; Pseudodifferential operators; Randomized algorithms; System identification

Indexed keywords

ELLIPTIC OPERATOR; GRAM MATRICES; HIGH PROBABILITY; LARGE DEVIATIONS; LINEAR COMBINATIONS; LINEAR OPERATORS; PRECONDITIONERS; PSEUDO DIFFERENTIAL; PSEUDO-DIFFERENTIAL OPERATOR; RANDOM VECTORS; RANDOMIZED ALGORITHMS; SEISMIC IMAGING;

IDENTIFICATION (CONTROL SYSTEMS); LINEAR SYSTEMS; MATHEMATICAL OPERATORS; NATURAL GAS CONDITIONING;

MATRIX ALGEBRA;

EID: 84861408239     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/110825972     Document Type: Article

References (26)

1. C. Andrieu, N. De Freitas, A. Doucet, and M.I. Jordan, An introduction to MCMC for machine learning, Machine Learning, 50 (2003), pp. 5-43.
2. M.A. Arcones and E. Giné, On decoupling, series expansions, and tail behavior of chaos processes, J. Theoret. Probab., 6 (1993), pp. 101-122.
3. A. Buchholz, Operator khintchine inequality in non-commutative probability, Math. Ann., 319 (2001), pp. 1-16.
4. E.J. Candes, J.K. Romberg, and T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Comm. Pure Appl. Math., 59 (2006), pp. 1207-1223. (Pubitemid 43988295)
5. T.F.C. Chan and T.P. Mathew, The interface probing technique in domain decomposition, SIAM J. Matrix Anal. Appl., 13 (1992), p. 212.
6. T.F. Chan and D.C. Resasco, A Survey of Preconditioners for Domain Decomposition, Technical report, DTIC Document, Yale University, New Haven, CT, 1985.
7. E.C. Chang, S. Mallat, and C. Yap, Wavelet foveation, Appl Comput. Harmon. Anal., 9 (2000), pp. 312-335.
8. V. De la Peña and E. Giné, Decoupling: From Dependence to Independence, Springer-Verlag, New York, 1999.
9. L. Demanet, P.D. Létourneau, N. Boumal, H. Calandra, J. Chiu, and S. Snelson, Matrix probing: A randomized preconditioner for the wave-equation Hessian, Appl. Comput. Harmon. Anal., 32 (2012), pp. 155-168.
10. L. Demanet and L. Ying, Discrete symbol calculus, SIAM Rev., 53 (2011), pp. 71-104.
11. A. Edelman, Eigenvalues and Condition Numbers of Random Matrices, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1989.
12. G.B. Folland, Introduction to Partial Differential Equations, Princeton University Press, Princeton, NJ, 1995.
13. N. Hale, N.J. Higham, L.N. Trefethen, et al., Computing aα, log (a), and related matrix functions by contour integrals, SIAM J. Numer. Anal., 46 (2008), pp. 2505-2523.
14. N. Halko, P. Martinsson, and J. Tropp, Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions, SIAM Rev., 53 (2011), p. 217.
15. N.J. Higham, Functions of Matrices: Theory and Computation, SIAM, Philadelphia, 2008.
16. D.R. Karger and C. Stein, A new approach to the minimum cut problem, J. ACM, 43 (1996), pp. 601-640. (Pubitemid 126582607)
17. R.M. Karp and M.O. Rabin, Efficient randomized pattern-matching algorithms, IBM J. Res. Development, 31 (1987), pp. 249-260.
18. F. Lust-Piquard, Inégalités de Khintchine dans Cp, CR Acad. Sci. Paris, 303 (1986), pp. 289- 292.
19. F. Lust-Piquard and G. Pisier, Non-commutative Khintchine and Paley inequalities, Ark. Mat., 29 (1991), pp. 241-260.
20. G.E. Pfander and H. Rauhut, Sparsity in time-frequency representations, J. Fourier Anal. Appl., 16 (2010), pp. 233-260.
21. G.E. Pfander, H. Rauhut, and J. Tanner, Identification of matrices having a sparse representation, IEEE Trans. Signal Process., 56 (2008), pp. 5376-5388.
22. G.E. Pfander, H. Rauhut, and J.A. Tropp, The restricted isometry property for timefrequency structured random matrices, arXiv:1106.3184, 2011.
23. H. Rauhut, Circulant and Toeplitz matrices in compressed sensing, in Proceedings of SPARS'09, Saint-Malo, France, 2009.
24. H. Rauhut, Compressive sensing and structured random matrices, Theoret. Found. Numer. Methods Sparse Recovery, 9 (2010), pp. 1-92.
25. M.A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, New York, 2001.
26. J.A. Tropp, On the conditioning of random subdictionaries, Appl. Comput. Harmon. Anal., 25 (2008), pp. 1-24. (Pubitemid 351721018)