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Numerical analysis for the quadratic matrix equations from a modification of fixed‐point type
Author(s) -
HernándezVerón Miguel A.,
Romero Natalia
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5726
Subject(s) - mathematics , iterative method , quadratic equation , local convergence , convergence (economics) , matrix (chemical analysis) , fixed point , newton's method in optimization , chebyshev filter , newton's method , iterative and incremental development , mathematical optimization , mathematical analysis , nonlinear system , computer science , geometry , materials science , software engineering , composite material , physics , quantum mechanics , economics , economic growth
In this paper, we study the quadratic matrix equations. To improve the application of iterative schemes, we use a transform of the quadratic matrix equation into an equivalent fixed‐point equation. Then, we consider an iterative process of Chebyshev‐type to solve this equation. We prove that this iterative scheme is more efficient than Newton's method. Moreover, we obtain a local convergence result for this iterative scheme. We finish showing, by an application to noisy Wiener‐Hopf problems, that the iterative process considered is computationally more efficient than Newton's method.