Abstract
In this paper, we study the simplest quadratic matrix equation: . We transform this equation into an equivalent fixed‐point equation, and based on it, we construct the Krasnoselskij method. From this transformation, we can obtain iterative schemes more accurate than the successive approximation method. Moreover, under suitable conditions, we establish different results for the existence and localization of a solution for this equation with the Krasnoselskij method. Finally, we see numerically that the predictor–corrector iterative scheme, with the Krasnoselskij method as a predictor and the Newton method as corrector method, can improve the numerical application of the Newton method when approximating a solution of the quadratic matrix equation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
