Iterative methods to compute weighted normal pseudosolutions with positive definite weights

1998 ◽  
Vol 34 (2) ◽  
pp. 245-253 ◽  
Author(s):  
E. F. Galba
Keyword(s):  
Iterative Methods ◽  
Positive Definite ◽  
Weighted Normal Pseudosolutions

scholarly journals The Inversion-Free Iterative Methods for Solving the Nonlinear Matrix EquationX+AHX-1A+BHX-1B=I

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Na Huang ◽  
Changfeng Ma
Keyword(s):  
Iterative Methods ◽  
Matrix Equation ◽  
Positive Definite ◽  
Numerical Results ◽  
Iterative Schemes ◽  
Positive Definite Solution ◽  
Nonlinear Matrix ◽  
Definite Solution

We present two inversion-free iterative methods for computing the maximal positive definite solution of the equationX+AHX-1A+BHX-1B=I. We prove that the sequences generated by the two iterative schemes are monotonically increasing and bounded above. We also present some numerical results to compare our proposed methods with some previously developed inversion-free techniques for solving the same matrix equation.

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