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

scholarly journals A note on the Ritz method with an application to overtone stellar pulsation theory

1968 ◽  
Vol 8 (2) ◽  
pp. 275-286 ◽  
Author(s):  
A. L. Andrew
Keyword(s):  
Numerical Solution ◽  
Eigenvalue Problems ◽  
Ritz Method ◽  
Linear Operators ◽  
Matrix Equations ◽  
Infinite Dimensional ◽  
Stellar Pulsation ◽  
Finite Matrix ◽  
The Matrix ◽  
Matrix Eigenvalue Problems

The Ritz method reduces eigenvalue problems involving linear operators on infinite dimensional spaces to finite matrix eigenvalue problems. This paper shows that for a certain class of linear operators it is possible to choose the coordinate functions so that numerical solution of the matrix equations is considerably simplified, especially when the matrices are large. The method is applied to the problem of overtone pulsations of stars.

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

Solution of quadratic matrix equations

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

Numerical Solution of Large Scale Sparse Matrix Equations in Python

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 959-960
Author(s):  
Björn Baran ◽  
Martin Köhler ◽  
Nitin Prasad ◽  
Jens Saak
Keyword(s):  
Numerical Solution ◽  
Large Scale ◽  
Sparse Matrix ◽  
Matrix Equations

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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