Volume 2, Issue 0
On Two Iteration Methods for the Quadratic Matrix Equations

Z.-Z. Bai, X.-X. Guo & J.-F. Yin

Int. J. Numer. Anal. Mod., 2 (2005), pp. 114-122.

Published online: 2005-11

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  • Abstract

By simply transforming the quadratic matrix equation into an equivalent fixed-point equation, we construct a successive approximation method and a Newton's method based on this fixed-point equation. Under suitable conditions, we prove the local convergence of these two methods, as well as the linear convergence speed of the successive approximation method and the quadratic convergence speed of the Newton's method. Numerical results show that these new methods are accurate and effective when they are used to solve the quadratic matrix equation.

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@Article{IJNAM-2-114, author = {Bai , Z.-Z. and Guo , X.-X. and Yin , J.-F.}, title = {On Two Iteration Methods for the Quadratic Matrix Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {0}, pages = {114--122}, abstract = {

By simply transforming the quadratic matrix equation into an equivalent fixed-point equation, we construct a successive approximation method and a Newton's method based on this fixed-point equation. Under suitable conditions, we prove the local convergence of these two methods, as well as the linear convergence speed of the successive approximation method and the quadratic convergence speed of the Newton's method. Numerical results show that these new methods are accurate and effective when they are used to solve the quadratic matrix equation.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/951.html} }
TY - JOUR T1 - On Two Iteration Methods for the Quadratic Matrix Equations AU - Bai , Z.-Z. AU - Guo , X.-X. AU - Yin , J.-F. JO - International Journal of Numerical Analysis and Modeling VL - 0 SP - 114 EP - 122 PY - 2005 DA - 2005/11 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/951.html KW - AB -

By simply transforming the quadratic matrix equation into an equivalent fixed-point equation, we construct a successive approximation method and a Newton's method based on this fixed-point equation. Under suitable conditions, we prove the local convergence of these two methods, as well as the linear convergence speed of the successive approximation method and the quadratic convergence speed of the Newton's method. Numerical results show that these new methods are accurate and effective when they are used to solve the quadratic matrix equation.

Z.-Z. Bai, X.-X. Guo & J.-F. Yin. (1970). On Two Iteration Methods for the Quadratic Matrix Equations. International Journal of Numerical Analysis and Modeling. 2 (0). 114-122. doi:
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