HSS-like method for solving complex nonlinear Yang–Baxter matrix equation

Dehghan, Mehdi; Shirilord, Akbar

doi:10.1007/s00366-020-00947-7

Cited by 16 publications

(6 citation statements)

References 34 publications

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“…Matrix equations of the form (1) and (3) are potentially applicable in other related problems (see [20,21] and the inside references).…”

Section: Remarkmentioning

confidence: 99%

Mathematics and Poetry • Unification, Unity, Union

Nichita¹

2020

Sci

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We consider a multitude of topics in mathematics where unification constructions play an important role: the Yang–Baxter equation and its modified version, Euler’s formula for dual numbers, means and their inequalities, topics in differential geometry, etc. It is interesting to observe that the idea of unification (unity and union) is also present in poetry. Moreover, Euler’s identity is a source of inspiration for the post-modern poets.

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“…Matrix equations of the form (1) and (3) are potentially applicable in other related problems (see [20,21] and the inside references).…”

Section: Remarkmentioning

confidence: 99%

Mathematics and Poetry • Unification, Unity, Union

Nichita¹

2020

Sci

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“…Remark 3. Matrix equations of the form (1) and ( 3) are potentially applicable in other related problems (see [20,21] and the inside references).…”

Section: Modified Yang-baxter Equationmentioning

confidence: 99%

Mathematics and Poetry • Unification, Unity, Union

Nichita

2020

Sci

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“…In [42], Dehghan et al presented a modified HSS scheme for solving symmetric linear systems. Moreover, Dehghan and Shirilord introduced a scheme based on the HSS to solve the Yang-Baxter matrix equation, complex Sylvester matrix equation, and absolute value matrix equation [43][44][45]. In 2005, by simply transforming the quadratic matrix equation into an equivalent fixed-point equation, a successive approximation method and Newton's method were made based on this fixed-point equation [46].…”

Section: Introductionmentioning

confidence: 99%

Developing HSS iteration schemes for solving the quadratic matrix equation AX2+BX+C=0$AX^{2}+BX+C=0$

Erfanifar,

Hajarian

2023

IET Control Theory & Appl

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The quadratic matrix equation (QME) occurs in the branches such as the quadratic eigenvalue problems and quasi‐birth‐death processes. Also, the numerical solution of QMEs is an essential step in many computational methods for linear‐quadratic and robust control, filtering, controller order reduction, inner‐outer factorization, spectral factorization, and other applications. In this study, schemes are presented to solve the QME based on the Hermitian and skew‐Hermitian splitting (HSS). It is shown that the proposed schemes converge to the solutions of the QME. Finally, some examples are solved to discover the application of the schemes in comparison with Newton's method.

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HSS-like method for solving complex nonlinear Yang–Baxter matrix equation

Cited by 16 publications

References 34 publications

Mathematics and Poetry • Unification, Unity, Union

Mathematics and Poetry • Unification, Unity, Union

Mathematics and Poetry • Unification, Unity, Union

Developing HSS iteration schemes for solving the quadratic matrix equation AX2+BX+C=0$AX^{2}+BX+C=0$

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