Alternately Linearized Implicit Iteration Methods for Solving Quadratic Matrix Equations

2014 ◽  
Vol 32 (3) ◽  
pp. 306-311
Author(s):  
Bing Gui
Keyword(s):  
Matrix Equations ◽  
Iteration Methods ◽  
Quadratic Matrix ◽  
Implicit Iteration

scholarly journals Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 218
Author(s):  
Lu-Chuan Ceng ◽  
Xiaoye Yang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mappings ◽  
General System ◽  
Inequality Constraint ◽  
Common Solution ◽  
Iteration Methods ◽  
Monotone Variational Inequality ◽  
Implicit Iteration

This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping in Hilbert spaces, which is called the triple hierarchical constrained variational inequality (THCVI), and introduces some Mann-type implicit iteration methods for solving it. Norm convergence of the proposed methods of the iteration methods is guaranteed under some suitable assumptions.

Transforming algebraic Riccati equations into unilateral quadratic matrix equations

2010 ◽  
Vol 116 (4) ◽  
pp. 553-578 ◽  
Author(s):  
Dario A. Bini ◽  
Beatrice Meini ◽  
Federico Poloni
Keyword(s):  
Riccati Equations ◽  
Matrix Equations ◽  
Algebraic Riccati Equations ◽  
Quadratic Matrix

A unified framework for the numerical solution of general quadratic matrix equations

2007 ◽  
Vol 24 (2) ◽  
pp. 259-287 ◽  
Author(s):  
Vassilios A. Tsachouridis ◽  
Nicos Karcanias ◽  
Ian Postlethwaite
Keyword(s):  
Numerical Solution ◽  
Matrix Equations ◽  
Unified Framework ◽  
Quadratic Matrix

Solution of quadratic matrix equations

1966 ◽  
Vol 2 (10) ◽  
pp. 371 ◽  
Author(s):  
B.D.O. Anderson
Keyword(s):  
Matrix Equations ◽  
Quadratic Matrix

Solving a class of quadratic matrix equations

2018 ◽  
Vol 82 ◽  
pp. 58-63 ◽  
Author(s):  
Mansour Saeed Ibrahim Adam ◽  
Jiu Ding ◽  
Qianglian Huang ◽  
Lanping Zhu
Keyword(s):  
Matrix Equations ◽  
Quadratic Matrix
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