Global Journal of Pure and Applied Mathematics
  • Year: 2005
  • Volume: 1
  • Issue: 2

On Iterative Algorithms for Solving the Matrix Equation X + A*X−1A = I

  • Author:
  • Salah M. El-Sayed1
  • Total Page Count: 13
  • Page Number: 203 to 215

Department of Mathematics, Faculty of Science, Benha university, Benha 13518, Egypt. E-mail: ms4elsayed@yahoo.com

1Mail address: Department of Mathematics, Scientific Departments, Education College for Girls, AlMontazah, Buraydah, AlQassim, Kingdom of Saudi Arabia.

1991 Mathematics Subject Classification: Primary 15A24, 65F10; Secondary 65H10, 93B40.

Abstract

This paper proposes iterative algorithms for the matrix equation X + A*X−1A = I. The rate of convergence of some algorithms suggested in [5] are obtained. An algorithm suggested in [5] which avoid the inverse calculations for each iteration is modified. The results show that this modified algorithm converges twice as fast as the original one. Numerical examples are presented which illustrate the effectiveness of the modified algorithms.

Keywords

Nonlinear matrix equation, iterative methods, convergence of sequences, positive definite solution