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Volume 32, Issue 3
Alternately Linearized Implicit Iteration Methods for Solving Quadratic Matrix Equations

Bing Gui, Hao Liu & Minli Yan

DOI: 10.4208/jcm.1401-CR9

J. Comp. Math., 32 (2014), pp. 306-311.

Published online: 2014-06

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  • Abstract

A numerical solution of the quadratic matrix equations associated with a nonsingular $M$-matrix by using the alternately linearized implicit iteration method is considered. An iteration method for computing a nonsingular $M$-matrix solution of the quadratic matrix equations is developed, and its corresponding theory is given. Some numerical examples are provided to show the efficiency of the new method.

  • Keywords

Quadratic matrix equation, Alternately iteration, $M$-matrix, Matrix transformation.

  • AMS Subject Headings

65F10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-306, author = {Bing Gui, Hao Liu and Minli Yan}, title = {Alternately Linearized Implicit Iteration Methods for Solving Quadratic Matrix Equations}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {3}, pages = {306--311}, abstract = {

A numerical solution of the quadratic matrix equations associated with a nonsingular $M$-matrix by using the alternately linearized implicit iteration method is considered. An iteration method for computing a nonsingular $M$-matrix solution of the quadratic matrix equations is developed, and its corresponding theory is given. Some numerical examples are provided to show the efficiency of the new method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1401-CR9}, url = {http://global-sci.org/intro/article_detail/jcm/9888.html} }
TY - JOUR T1 - Alternately Linearized Implicit Iteration Methods for Solving Quadratic Matrix Equations AU - Bing Gui, Hao Liu & Minli Yan JO - Journal of Computational Mathematics VL - 3 SP - 306 EP - 311 PY - 2014 DA - 2014/06 SN - 32 DO - http://doi.org/10.4208/jcm.1401-CR9 UR - https://global-sci.org/intro/article_detail/jcm/9888.html KW - Quadratic matrix equation, Alternately iteration, $M$-matrix, Matrix transformation. AB -

A numerical solution of the quadratic matrix equations associated with a nonsingular $M$-matrix by using the alternately linearized implicit iteration method is considered. An iteration method for computing a nonsingular $M$-matrix solution of the quadratic matrix equations is developed, and its corresponding theory is given. Some numerical examples are provided to show the efficiency of the new method.

Bing Gui, Hao Liu and Minli Yan. (2014). Alternately Linearized Implicit Iteration Methods for Solving Quadratic Matrix Equations. Journal of Computational Mathematics. 32 (3). 306-311. doi:10.4208/jcm.1401-CR9
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