Absolute value equations with tensor product structure: Unique solvability and numerical solution

Somayeh Mollahasani; Fatemeh Panjeh Ali Beik

Applications of Mathematics (2022)

  • Volume: 67, Issue: 5, page 657-674
  • ISSN: 0862-7940

Abstract

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We consider the absolute value equations (AVEs) with a certain tensor product structure. Two aspects of this kind of AVEs are discussed in detail: the solvability and approximate solution. More precisely, first, some sufficient conditions are provided which guarantee the unique solvability of this kind of AVEs. Furthermore, a new iterative method is constructed for solving AVEs and its convergence properties are investigated.  The validity of established theoretical results and performance of the proposed iterative scheme are examined numerically. 

How to cite

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Mollahasani, Somayeh, and Panjeh Ali Beik, Fatemeh. "Absolute value equations with tensor product structure: Unique solvability and numerical solution." Applications of Mathematics 67.5 (2022): 657-674. <http://eudml.org/doc/298493>.

@article{Mollahasani2022,
abstract = {We consider the absolute value equations (AVEs) with a certain tensor product structure. Two aspects of this kind of AVEs are discussed in detail: the solvability and approximate solution. More precisely, first, some sufficient conditions are provided which guarantee the unique solvability of this kind of AVEs. Furthermore, a new iterative method is constructed for solving AVEs and its convergence properties are investigated.  The validity of established theoretical results and performance of the proposed iterative scheme are examined numerically. },
author = {Mollahasani, Somayeh, Panjeh Ali Beik, Fatemeh},
journal = {Applications of Mathematics},
keywords = {iterative method; absolute value equation; convergence; tensor (Kronecker) product},
language = {eng},
number = {5},
pages = {657-674},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Absolute value equations with tensor product structure: Unique solvability and numerical solution},
url = {http://eudml.org/doc/298493},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Mollahasani, Somayeh
AU - Panjeh Ali Beik, Fatemeh
TI - Absolute value equations with tensor product structure: Unique solvability and numerical solution
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 5
SP - 657
EP - 674
AB - We consider the absolute value equations (AVEs) with a certain tensor product structure. Two aspects of this kind of AVEs are discussed in detail: the solvability and approximate solution. More precisely, first, some sufficient conditions are provided which guarantee the unique solvability of this kind of AVEs. Furthermore, a new iterative method is constructed for solving AVEs and its convergence properties are investigated.  The validity of established theoretical results and performance of the proposed iterative scheme are examined numerically. 
LA - eng
KW - iterative method; absolute value equation; convergence; tensor (Kronecker) product
UR - http://eudml.org/doc/298493
ER -

References

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