Nondefinite least squares and its relation to H/sub infinity /-minimum error state estimation

1991 ◽  
Vol 36 (12) ◽  
pp. 1469-1472 ◽  
Author(s):  
I. Yaesh ◽  
U. Shaked
Keyword(s):  
Least Squares ◽  
State Estimation ◽  
Minimum Error ◽  
Error State

scholarly journals Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adisorn Kittisopaporn ◽  
Pattrawut Chansangiam
Keyword(s):  
Least Squares ◽  
Iterative Algorithm ◽  
Gradient Descent ◽  
Main Idea ◽  
Full Column Rank ◽  
Minimum Error ◽  
Matrix Coefficients ◽  
Special Cases ◽  
Efficiency And Effectiveness ◽  
Associated Matrix

AbstractThis paper proposes an effective gradient-descent iterative algorithm for solving a generalized Sylvester-transpose equation with rectangular matrix coefficients. The algorithm is applicable for the equation and its interesting special cases when the associated matrix has full column-rank. The main idea of the algorithm is to have a minimum error at each iteration. The algorithm produces a sequence of approximated solutions converging to either the unique solution, or the unique least-squares solution when the problem has no solution. The convergence analysis points out that the algorithm converges fast for a small condition number of the associated matrix. Numerical examples demonstrate the efficiency and effectiveness of the algorithm compared to renowned and recent iterative methods.

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