A fractional Landweber iterative regularization method for stable analytic continuation
In this paper, we consider the problem of analytic continuation of the analytic function $g(z) = g(x+iy)$ on a strip domain Ω = $\{z = x+iy\in \mathbb{C}|\, x\in\mathbb{R}, 0 < y < y_0\}$, where the data is given only on the line $y = 0$. This problem is a severely ill-posed problem. We propos...
Saved in:
| Published in | AIMS mathematics Vol. 6; no. 1; pp. 404 - 419 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
AIMS Press
01.01.2021
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 2473-6988 2473-6988 |
| DOI | 10.3934/math.2021025 |
Cover
| Abstract | In this paper, we consider the problem of analytic continuation of the analytic function $g(z) = g(x+iy)$ on a strip domain Ω = $\{z = x+iy\in \mathbb{C}|\, x\in\mathbb{R}, 0 < y < y_0\}$, where the data is given only on the line $y = 0$. This problem is a severely ill-posed problem. We propose the fraction Landweber iterative regularization method to deal with this problem. Under the a priori and a posteriori regularization parameter choice rule, we all obtain the error estimates between the regularization solution and the exact solution. Some numerical examples are given to verify the efficiency and accuracy of the proposed methods. |
|---|---|
| AbstractList | In this paper, we consider the problem of analytic continuation of the analytic function $g(z)=g(x+iy)$ on a strip domain Ω=$\{z=x+iy\in \mathbb{C}|\,x\in\mathbb{R},0< y < y_0\}$, where the data is given only on the line $y=0$. This problem is a severely ill-posed problem. We propose the fraction Landweber iterative regularization method to deal with this problem. Under the a priori and a posteriori regularization parameter choice rule, we all obtain the error estimates between the regularization solution and the exact solution. Some numerical examples are given to verify the efficiency and accuracy of the proposed methods. |
| Author | Wang, Qianchao Li, Xiaoxiao Yang, Fan |
| Author_xml | – sequence: 1 givenname: Fan surname: Yang fullname: Yang, Fan – sequence: 2 givenname: Qianchao surname: Wang fullname: Wang, Qianchao – sequence: 3 givenname: Xiaoxiao surname: Li fullname: Li, Xiaoxiao |
| BookMark | eNptUNtKAzEQDaJgrb75AfkAq7ntJvtYxBsUfFF8DJPspI1sN5JNFf16t1VBRBiYYeacw5lzRPb71CMhp5ydy0aqizWU1blggjNR7ZGJUFrO6saY_V_zITkZhmfGRpRQQqsJeZrTkMGXmHro6AL69g0dZhoLZijxFWnG5aaDHD9gC6JrLKvU0pAyHQq4DimMzPcSPfWpL7Hf7HDH5CBAN-DJd5-Sx-urh8vb2eL-5u5yvph5qU2ZOah95aUIxinktRKtq_14aiWOZYysGMqGBeV00EY5w3WoQwuNN5y5xskpufvSbRM825cc15DfbYJod4uUlxbyaK5Dq6vAsTEOuZaKOQkMW-VZYF7oqtJm1BJfWj6nYcgYrI9l903JEDvLmd0mbbdJ2--kR9LZH9KPiX_hn6rhhAc |
| CitedBy_id | crossref_primary_10_1016_j_camwa_2023_07_009 crossref_primary_10_3390_math9182255 crossref_primary_10_1007_s11075_024_01815_x crossref_primary_10_3390_sym14061209 crossref_primary_10_1016_j_amc_2024_128948 |
| Cites_doi | 10.1186/s13661-017-0823-8 10.1080/17415977.2013.780167 10.1016/j.matcom.2011.08.005 10.1137/0911007 10.1080/17415977.2017.1384825 10.1007/s11075-019-00734-6 10.1063/1.527285 10.1186/s13662-017-1423-8 10.1016/j.apnum.2017.08.004 10.1088/1361-6420/ab730b 10.1515/jiip.2000.8.1.23 10.1186/s13661-016-0733-1 10.1080/00207160.2014.920500 10.11948/20180279 10.1016/j.cam.2010.12.017 10.1137/080730196 10.1515/fca-2019-0039 10.1016/j.matcom.2010.11.011 10.1007/s00211-005-0622-5 10.1007/978-94-009-1740-8 10.1090/mmono/064 10.1088/0266-5611/24/4/045005 10.1016/j.amc.2014.01.053 10.1016/j.cam.2011.12.016 10.1088/0266-5611/24/6/065003 10.1016/j.cam.2017.06.014 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION DOA |
| DOI | 10.3934/math.2021025 |
| DatabaseName | CrossRef DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 2473-6988 |
| EndPage | 419 |
| ExternalDocumentID | oai_doaj_org_article_75f1e98be17340b3a0ed4c0f0c275578 10_3934_math_2021025 |
| GroupedDBID | AAYXX ADBBV ALMA_UNASSIGNED_HOLDINGS AMVHM BCNDV CITATION EBS FRJ GROUPED_DOAJ IAO ITC M~E OK1 RAN |
| ID | FETCH-LOGICAL-c378t-ba6c5c32f8b4e1642db6cc37d3ed3e88350e390f4b7f784b817f6fda9c810b9b3 |
| IEDL.DBID | DOA |
| ISSN | 2473-6988 |
| IngestDate | Wed Aug 27 01:18:19 EDT 2025 Tue Jul 01 03:56:46 EDT 2025 Thu Apr 24 23:07:26 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c378t-ba6c5c32f8b4e1642db6cc37d3ed3e88350e390f4b7f784b817f6fda9c810b9b3 |
| OpenAccessLink | https://doaj.org/article/75f1e98be17340b3a0ed4c0f0c275578 |
| PageCount | 16 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_75f1e98be17340b3a0ed4c0f0c275578 crossref_citationtrail_10_3934_math_2021025 crossref_primary_10_3934_math_2021025 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2021-01-01 |
| PublicationDateYYYYMMDD | 2021-01-01 |
| PublicationDate_xml | – month: 01 year: 2021 text: 2021-01-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | AIMS mathematics |
| PublicationYear | 2021 |
| Publisher | AIMS Press |
| Publisher_xml | – name: AIMS Press |
| References | key-10.3934/math.2021025-4 key-10.3934/math.2021025-5 key-10.3934/math.2021025-2 key-10.3934/math.2021025-3 key-10.3934/math.2021025-1 key-10.3934/math.2021025-20 key-10.3934/math.2021025-21 key-10.3934/math.2021025-22 key-10.3934/math.2021025-23 key-10.3934/math.2021025-24 key-10.3934/math.2021025-25 key-10.3934/math.2021025-26 key-10.3934/math.2021025-27 key-10.3934/math.2021025-8 key-10.3934/math.2021025-9 key-10.3934/math.2021025-10 key-10.3934/math.2021025-6 key-10.3934/math.2021025-11 key-10.3934/math.2021025-7 key-10.3934/math.2021025-12 key-10.3934/math.2021025-13 key-10.3934/math.2021025-14 key-10.3934/math.2021025-15 key-10.3934/math.2021025-16 key-10.3934/math.2021025-17 key-10.3934/math.2021025-18 key-10.3934/math.2021025-19 |
| References_xml | – ident: key-10.3934/math.2021025-20 doi: 10.1186/s13661-017-0823-8 – ident: key-10.3934/math.2021025-6 doi: 10.1080/17415977.2013.780167 – ident: key-10.3934/math.2021025-7 doi: 10.1016/j.matcom.2011.08.005 – ident: key-10.3934/math.2021025-2 doi: 10.1137/0911007 – ident: key-10.3934/math.2021025-22 doi: 10.1080/17415977.2017.1384825 – ident: key-10.3934/math.2021025-23 doi: 10.1007/s11075-019-00734-6 – ident: key-10.3934/math.2021025-3 doi: 10.1063/1.527285 – ident: key-10.3934/math.2021025-19 doi: 10.1186/s13662-017-1423-8 – ident: key-10.3934/math.2021025-25 doi: 10.1016/j.apnum.2017.08.004 – ident: key-10.3934/math.2021025-11 doi: 10.1088/1361-6420/ab730b – ident: key-10.3934/math.2021025-4 doi: 10.1515/jiip.2000.8.1.23 – ident: key-10.3934/math.2021025-21 doi: 10.1186/s13661-016-0733-1 – ident: key-10.3934/math.2021025-15 doi: 10.1080/00207160.2014.920500 – ident: key-10.3934/math.2021025-24 doi: 10.11948/20180279 – ident: key-10.3934/math.2021025-13 doi: 10.1016/j.cam.2010.12.017 – ident: key-10.3934/math.2021025-16 doi: 10.1137/080730196 – ident: key-10.3934/math.2021025-9 doi: 10.1515/fca-2019-0039 – ident: key-10.3934/math.2021025-12 doi: 10.1016/j.matcom.2010.11.011 – ident: key-10.3934/math.2021025-10 doi: 10.1007/s00211-005-0622-5 – ident: key-10.3934/math.2021025-18 doi: 10.1007/978-94-009-1740-8 – ident: key-10.3934/math.2021025-1 doi: 10.1090/mmono/064 – ident: key-10.3934/math.2021025-26 doi: 10.1088/0266-5611/24/4/045005 – ident: key-10.3934/math.2021025-14 doi: 10.1016/j.amc.2014.01.053 – ident: key-10.3934/math.2021025-8 doi: 10.1016/j.cam.2011.12.016 – ident: key-10.3934/math.2021025-27 – ident: key-10.3934/math.2021025-5 doi: 10.1088/0266-5611/24/6/065003 – ident: key-10.3934/math.2021025-17 doi: 10.1016/j.cam.2017.06.014 |
| SSID | ssj0002124274 |
| Score | 2.183668 |
| Snippet | In this paper, we consider the problem of analytic continuation of the analytic function $g(z) = g(x+iy)$ on a strip domain Ω = $\{z = x+iy\in \mathbb{C}|\,... In this paper, we consider the problem of analytic continuation of the analytic function $g(z)=g(x+iy)$ on a strip domain Ω=$\{z=x+iy\in... |
| SourceID | doaj crossref |
| SourceType | Open Website Enrichment Source Index Database |
| StartPage | 404 |
| SubjectTerms | fractional landweber regularization method ill-posed problem inverse problem stable analytic continuation |
| Title | A fractional Landweber iterative regularization method for stable analytic continuation |
| URI | https://doaj.org/article/75f1e98be17340b3a0ed4c0f0c275578 |
| Volume | 6 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: Directory of Open Access Journals customDbUrl: eissn: 2473-6988 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0002124274 issn: 2473-6988 databaseCode: DOA dateStart: 20160101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2473-6988 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0002124274 issn: 2473-6988 databaseCode: M~E dateStart: 20160101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1NS8QwEA2yJz2In7h-kYOepGzbpEl6XMVlEdeTi3srmXQCwlKlrv_fSVOX9SBehB5KO4QwEybvtZM3jF3VtvSqkJAASpFIpVxSanCJIvjsZe2N7ZrBzJ7UdC4fFsVio9VXqAmL8sDRcSNd-AxLA5hpIVMQNsVautSnLtcFLbeQfWkb2yBTIQdTQpbEt2KluyiFHBH-C_8eAsMpfuxBG1L93Z4y2WO7PRjk4ziJfbaFzQHbma2VVD8O2cuY-zYePiDLR-L9lPew5VENmVIVb7tu8m1_npLHltCcsCgn4AdL5DbojtBoPJSlvzZR2_uIzSf3z3fTpG-GkDihzSoBq1zhRO4NSCSOk9egHL2qBdJlCEilKMrUS9BeGwkm0155CoUzWQoliGM2aN4aPGFcOJln6ETt6E4B2AycJWpRo9IUNxyym2_3VK5XCg8NK5YVMYbgzCo4s-qdOWTXa-v3qJDxi91t8PTaJuhadw8o2lUf7eqvaJ_-xyBnbDvMKX5IOWeDVfuJFwQtVnDZraIvrxXPAQ |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+fractional+Landweber+iterative+regularization+method+for+stable+analytic+continuation&rft.jtitle=AIMS+mathematics&rft.au=Fan+Yang&rft.au=Qianchao+Wang&rft.au=Xiaoxiao+Li&rft.date=2021-01-01&rft.pub=AIMS+Press&rft.eissn=2473-6988&rft.volume=6&rft.issue=1&rft.spage=404&rft.epage=419&rft_id=info:doi/10.3934%2Fmath.2021025&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_75f1e98be17340b3a0ed4c0f0c275578 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2473-6988&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2473-6988&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2473-6988&client=summon |