The homogeneous projective transformation of general quadratic matrix equations |
| |
Authors: | Tsachouridis Vassilios A; Kouvaritakis Basil |
| |
Institution: |
Department of Engineering Science, University of Oxford, 17 Parks Road, Oxford, OX1 3PJ, UK
|
| |
Abstract: | ** Email: vassilios.tsachouridis{at}ieee.org*** Email: basil.kouvaritakis{at}eng.ox.ac.uk Algebraic quadratic equations are a special case of a singlegeneralized algebraic quadratic matrix equation (GQME). Hence,the importance of that equation in science and engineering isevident. This paper focus on the study of solutions of thatGQME and a unified framework for the characterization and identificationof solutions at infinity and of finite solutions of generalquadratic algebraic matrix equations is presented. The analysisis based on the concept of homogeneous projective transformationfor general polynomial systems (Morgan, 1986). In addition,a numerical error analysis for the computed solutions is providedfor the assessment of numerical accuracy, stability and conditioningof the computed solutions. The proposed framework is independentof any numerical method and therefore it can be used along withvarious possible numerical methods for the GQME solution, especiallymatrix flow-based algorithms (Chu, 1994) (e.g. continuation/homotopy,Morgan, 1989). |
| |
Keywords: | matrix equations homogeneous projective transformation perturbation analysis condition numbers forward/backward error roundoff error numerical accuracy numerical stability |
本文献已被 Oxford 等数据库收录! |
|