Column subset selection, matrix factorization, and eigenvalue optimization

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2009, Pages 978-986

  Tropp, Joel A ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; FACTORIZATION; FUNCTIONAL ANALYSIS; POLYNOMIAL APPROXIMATION;

COLUMN SELECTIONS; EIGENVALUE OPTIMIZATION; MATRIX FACTORIZATIONS; NUMERICAL LINEAR ALGEBRA; POLYNOMIAL-TIME ALGORITHMS; RANK-REVEALING QR; SEMIDEFINITE PROGRAMS; SPECTRAL PROPERTIES;

MATRIX ALGEBRA;

EID: 70349135853     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973068.106     Document Type: Conference Paper

References (16)

1. [Ali95] F. Alizadeh. Interior-point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Optimization, 5(1):13-51, Feb. 1995.
2. [AN04] N. Alon and A. Naor. Approximating the cut norm via Grothendieck's inequality. In Proc. 36th Ann. ACM Symposium on Theory of Computing (STOC), pages 72-80, Chicago, 2004.
3. [BDM08] C. Boutsidis, P. Drineas, and M. Mahoney. On selecting exactly k columns from a matrix. Submitted for publication, 2008.
4. [BT87] J. Bourgain and L. Tzafriri. Invertibility of "large" submatrices with applications to the geometry of Banach spaces and harmonic analysis. Israel J. Math, 57(2):137-224, 1987.
5. [BT91] J. Bourgain and L. Tzafriri. On a problem of Kadison and Singer. J. reine angew. Math., 420:1-43, 1991.
6. [BT03] A. Beck and M. Teboulle. Mirror descent and nonlinear projected subgradient methods for convex optimization. Operations Res. Lett., 31:167-175, 2003.
7. [GE96] M. Gu and S. Eisenstat. Efficient algorithms for computing a strong rank-revealing QR factorization. SIAM J. Sci. Comput., 17(4):848-869, Jul. 1996.
8. [GW95] M. X. Goemans and D. P. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. Assoc. Comput. Mach., 42:1115-1145, 1995.
9. [HJ85] R. A. Horn and C. R. Johnson. Matrix Analysis. Cambridge Univ. Press, 1985.
10. [LO96] A. S. Lewis and M. L. Overton. Eigenvalue optimization. Acta Numerica, 5:149-190, 1996.
11. [Pis86] G. Pisier. Factorization of linear operators and geometry of Banach spaces. Number 60 in CBMS Regional Conference Series in Mathematics. AMS, Providence, 1986. Reprinted with corrections, 1987.
12. ∞,1 is NP-hard. Linear and Multilinear Algebra, 47:195-204, 2000.
13. [RV07] M. Rudelson and R. Vershynin. Sampling from large matrices: An approach through geometric functional analysis. J. Amer. Comput. Soc., 54(4):Article 21, pp. 1-19, Jul. 2007.
14. n and random matrices. Amer. J. Math., 112(6):899-942, Dec. 1990.
15. [Tro08] J. A. Tropp. Column subset selection, matrix factorization, and eigenvalue optimization. ACM Technical Report 2008-2102, California Institute of Technology, 2008.
16. [Ver01] R. Vershynin. Johns decompositions: Selecting a large part. Israel J. Math., 122:253-277, 2001.