Positive definite combination of symmetric matrices

  • Authors:
  • A. Zaidi

  • Affiliations:
  • Dept. de Math., Inst. Nat. des Sci. Appliquees et de Technol., Tunis, Tunisia

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2005

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Abstract

This correspondence presents a new algorithm to find a positive definite combination of some given real symmetric matrices. When this problem has solutions, we show that it can be written as an optimization problem. An iterative algorithm using a relaxation type method is proposed to solve this optimization problem. We also prove that this algorithm has a finite-step global convergence property. A comparison, by computer simulations, shows that our algorithm is much faster than another one generally proposed in literature to find such a combination.