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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 435730, 8 pages
Geometrical and Spectral Properties of the Orthogonal Projections of the Identity
Department of Mathematics, Research Institute SIANI, University of Las Palmas de Gran Canaria, Campus de Tafira, 35017 Las Palmas de Gran Canaria, Spain
Received 28 December 2012; Accepted 10 April 2013
Academic Editor: K. Sivakumar
Copyright © 2013 Luis González et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- O. Axelsson, Iterative Solution Methods, Cambridge University Press, Cambridge, Mass, USA, 1994.
- Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing, Boston, Mass, USA, 1996.
- S.-L. Wu, F. Chen, and X.-Q. Niu, “A note on the eigenvalue analysis of the SIMPLE preconditioning for incompressible flow,” Journal of Applied Mathematics, vol. 2012, Article ID 564132, 7 pages, 2012.
- M. Benzi, “Preconditioning techniques for large linear systems: a survey,” Journal of Computational Physics, vol. 182, no. 2, pp. 418–477, 2002.
- G. Montero, L. González, E. Flórez, M. D. García, and A. Suárez, “Approximate inverse computation using Frobenius inner product,” Numerical Linear Algebra with Applications, vol. 9, no. 3, pp. 239–247, 2002.
- A. Suárez and L. González, “A generalization of the Moore-Penrose inverse related to matrix subspaces of ,” Applied Mathematics and Computation, vol. 216, no. 2, pp. 514–522, 2010.
- E. Chow and Y. Saad, “Approximate inverse preconditioners via sparse-sparse iterations,” SIAM Journal on Scientific Computing, vol. 19, no. 3, pp. 995–1023, 1998.
- E. Chow and Y. Saad, “Approximate inverse techniques for block-partitioned matrices,” SIAM Journal on Scientific Computing, vol. 18, no. 6, pp. 1657–1675, 1997.
- R. M. Holland, A. J. Wathen, and G. J. Shaw, “Sparse approximate inverses and target matrices,” SIAM Journal on Scientific Computing, vol. 26, no. 3, pp. 1000–1011, 2005.
- R. Andreani, M. Raydan, and P. Tarazaga, “On the geometrical structure of symmetric matrices,” Linear Algebra and Its Applications, vol. 438, no. 3, pp. 1201–1214, 2013.
- L. González, “Orthogonal projections of the identity: spectral analysis and applications to approximate inverse preconditioning,” SIAM Review, vol. 48, no. 1, pp. 66–75, 2006.
- A. Suárez and L. González, “Normalized Frobenius condition number of the orthogonal projections of the identity,” Journal of Mathematical Analysis and Applications, vol. 400, no. 2, pp. 510–516, 2013.
- J.-P. Chehab and M. Raydan, “Geometrical properties of the Frobenius condition number for positive definite matrices,” Linear Algebra and Its Applications, vol. 429, no. 8-9, pp. 2089–2097, 2008.
- M. L. Buzano, “Generalizzazione della diseguaglianza di Cauchy-Schwarz,” Rendiconti del Seminario Matematico Università e Politecnico di Torino, vol. 31, pp. 405–409, 1974 (Italian).
- M. R. Hestenes and E. Stiefel, “Methods of conjugate gradients for solving linear systems,” Journal of Research of the National Bureau of Standards, vol. 49, no. 6, pp. 409–436, 1952.
- R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK, 1991.
- E. H. Lieb and W. Thirring, “Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities,” in Studies in Mathematical Physics: Essays in Honor of Valentine Bargmann, E. Lieb, B. Simon, and A. Wightman, Eds., pp. 269–303, Princeton University Press, Princeton, NJ, USA, 1976.
- Z. Ulukök and R. Türkmen, “On some matrix trace inequalities,” Journal of Inequalities and Applications, vol. 2010, Article ID 201486, 8 pages, 2010.
- R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.