Minimal condition number for positive definite Hankel matrices using semidefinite programming

Minimal condition number for positive definite Hankel matrices using semidefinite programming

Article history: Received 27 January 2009 Accepted 15 April 2010 Available online 26 June 2010 Submitted by V. Mehrmann

On The Frobenius Condition Number of Positive Definite Matrices

Singular value inequalities for positive semidefinite matrices

In this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl‎. ‎308 (2000) 203-211] and [Linear Algebra Appl‎. ‎428 (2008) 2177-2191]‎.

Semidefinite Programming in the Space of Partial Positive Semidefinite Matrices

We build upon the work of Fukuda et al. [SIAM J. Optim., 11 (2001), pp. 647–674] and Nakata et al. [Math. Program., 95 (2003), pp. 303–327], in which the theory of partial positive semidefinite matrices was applied to the semidefinite programming (SDP) problem as a technique for exploiting sparsity in the data. In contrast to their work, which improved an existing algorithm based on a standard ...

singular value inequalities for positive semidefinite matrices

in this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎our results are similar to some inequalities shown by bhatia and kittaneh in [linear algebra appl‎. ‎308 (2000) 203-211] and [linear algebra appl‎. ‎428 (2008) 2177-2191]‎.