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Investigation of positive definite solution of nonlinear matrix equation Xp=Q+∑i=1mAi∗XδAi
In this paper, we consider the nonlinear matrix equation X p = Q + ∑ i = 1 m A i ∗ X δ A i , where A i ( i = 1 , 2 , … , m ) are n × n nonsingular complex matrices, Q is a n × n Hermitian positive definite (HPD) matrix, p ≥ 1 , m ≥ 1 are positive integers, and δ ∈ ( 0 , 1 ) . We discuss the solution...
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| Published in: | Computational & applied mathematics 2021, Vol.40 (3) |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| container_title | Computational & applied mathematics |
| container_volume | 40 |
| creator | Jin, Zhixiang Zhai, Chengbo |
| description | In this paper, we consider the nonlinear matrix equation
X
p
=
Q
+
∑
i
=
1
m
A
i
∗
X
δ
A
i
,
where
A
i
(
i
=
1
,
2
,
…
,
m
)
are
n
×
n
nonsingular complex matrices,
Q
is a
n
×
n
Hermitian positive definite (HPD) matrix,
p
≥
1
,
m
≥
1
are positive integers, and
δ
∈
(
0
,
1
)
. We discuss the solution of this equation via properties of Thompson metric and two fixed point theorems in ordered Banach spaces and estimate the bounds of the HPD solution. Furthermore, perturbation analysis is investigated. |
| doi_str_mv | 10.1007/s40314-021-01463-0 |
| format | article |
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X
p
=
Q
+
∑
i
=
1
m
A
i
∗
X
δ
A
i
,
where
A
i
(
i
=
1
,
2
,
…
,
m
)
are
n
×
n
nonsingular complex matrices,
Q
is a
n
×
n
Hermitian positive definite (HPD) matrix,
p
≥
1
,
m
≥
1
are positive integers, and
δ
∈
(
0
,
1
)
. We discuss the solution of this equation via properties of Thompson metric and two fixed point theorems in ordered Banach spaces and estimate the bounds of the HPD solution. Furthermore, perturbation analysis is investigated.</description><identifier>ISSN: 2238-3603</identifier><identifier>EISSN: 1807-0302</identifier><identifier>DOI: 10.1007/s40314-021-01463-0</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Applications of Mathematics ; Applied physics ; Banach spaces ; Computational mathematics ; Computational Mathematics and Numerical Analysis ; Fixed points (mathematics) ; Mathematical analysis ; Mathematical Applications in Computer Science ; Mathematical Applications in the Physical Sciences ; Mathematics ; Mathematics and Statistics ; Matrix methods ; Perturbation methods</subject><ispartof>Computational & applied mathematics, 2021, Vol.40 (3)</ispartof><rights>SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2021</rights><rights>SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Jin, Zhixiang</creatorcontrib><creatorcontrib>Zhai, Chengbo</creatorcontrib><title>Investigation of positive definite solution of nonlinear matrix equation Xp=Q+∑i=1mAi∗XδAi</title><title>Computational & applied mathematics</title><addtitle>Comp. Appl. Math</addtitle><description>In this paper, we consider the nonlinear matrix equation
X
p
=
Q
+
∑
i
=
1
m
A
i
∗
X
δ
A
i
,
where
A
i
(
i
=
1
,
2
,
…
,
m
)
are
n
×
n
nonsingular complex matrices,
Q
is a
n
×
n
Hermitian positive definite (HPD) matrix,
p
≥
1
,
m
≥
1
are positive integers, and
δ
∈
(
0
,
1
)
. We discuss the solution of this equation via properties of Thompson metric and two fixed point theorems in ordered Banach spaces and estimate the bounds of the HPD solution. Furthermore, perturbation analysis is investigated.</description><subject>Applications of Mathematics</subject><subject>Applied physics</subject><subject>Banach spaces</subject><subject>Computational mathematics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Fixed points (mathematics)</subject><subject>Mathematical analysis</subject><subject>Mathematical Applications in Computer Science</subject><subject>Mathematical Applications in the Physical Sciences</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrix methods</subject><subject>Perturbation methods</subject><issn>2238-3603</issn><issn>1807-0302</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkE1OwzAQRi0EEqVwAVaRWCLD2OPE8aKLquKnUiWE1EV3lps6lavWSeOk4gjddsVFOAeH6EkIBMRqFt_7ZjSPkGsGdwxA3gcByAQFzigwkSCFE9JjKUgKCPyU9DjHlGICeE4uQlgBoGRC9Ige-50NtVua2hU-KvKoLIKr3c5GC5s772obhWLd_KW-8Gvnramijakr9xbZbdNVZ-Xg9fa4P7gB2wzdcf8--_wYuktylpt1sFe_s0-mjw_T0TOdvDyNR8MJLSUHahRCxjHjc7BxjDxnQhpMrEoxVW2iJE8yiJN5zJBlBhlTUiWZyWCuYBEn2Cc33dqyKrZN-5BeFU3l24uaCyUlFxCrlsKOCmXl_NJW_xQD_S1SdyJ1K1L_iNSAXycwZ90</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Jin, Zhixiang</creator><creator>Zhai, Chengbo</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>2021</creationdate><title>Investigation of positive definite solution of nonlinear matrix equation Xp=Q+∑i=1mAi∗XδAi</title><author>Jin, Zhixiang ; Zhai, Chengbo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p720-a930c23c2b0e5532f147a36e983890c29726c056b5131ca3119796cac0b90d563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Applications of Mathematics</topic><topic>Applied physics</topic><topic>Banach spaces</topic><topic>Computational mathematics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Fixed points (mathematics)</topic><topic>Mathematical analysis</topic><topic>Mathematical Applications in Computer Science</topic><topic>Mathematical Applications in the Physical Sciences</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Matrix methods</topic><topic>Perturbation methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jin, Zhixiang</creatorcontrib><creatorcontrib>Zhai, Chengbo</creatorcontrib><jtitle>Computational & applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jin, Zhixiang</au><au>Zhai, Chengbo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Investigation of positive definite solution of nonlinear matrix equation Xp=Q+∑i=1mAi∗XδAi</atitle><jtitle>Computational & applied mathematics</jtitle><stitle>Comp. Appl. Math</stitle><date>2021</date><risdate>2021</risdate><volume>40</volume><issue>3</issue><issn>2238-3603</issn><eissn>1807-0302</eissn><abstract>In this paper, we consider the nonlinear matrix equation
X
p
=
Q
+
∑
i
=
1
m
A
i
∗
X
δ
A
i
,
where
A
i
(
i
=
1
,
2
,
…
,
m
)
are
n
×
n
nonsingular complex matrices,
Q
is a
n
×
n
Hermitian positive definite (HPD) matrix,
p
≥
1
,
m
≥
1
are positive integers, and
δ
∈
(
0
,
1
)
. We discuss the solution of this equation via properties of Thompson metric and two fixed point theorems in ordered Banach spaces and estimate the bounds of the HPD solution. Furthermore, perturbation analysis is investigated.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40314-021-01463-0</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2238-3603 |
| ispartof | Computational & applied mathematics, 2021, Vol.40 (3) |
| issn | 2238-3603 1807-0302 |
| language | eng |
| recordid | cdi_proquest_journals_2497724059 |
| source | Springer Link |
| subjects | Applications of Mathematics Applied physics Banach spaces Computational mathematics Computational Mathematics and Numerical Analysis Fixed points (mathematics) Mathematical analysis Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics Matrix methods Perturbation methods |
| title | Investigation of positive definite solution of nonlinear matrix equation Xp=Q+∑i=1mAi∗XδAi |
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