View in EDS HTML Full Text PDF Full Text

An improved Tikhonov regularization method combined with the exponential filter function.

Saved in:
Bibliographic Details
Title: An improved Tikhonov regularization method combined with the exponential filter function.
Authors: Zeng, Xiaoniu1 (AUTHOR) xiaoniuzeng@163.com, Liu, Tianyou1 (AUTHOR), Tan, Xiaofeng1 (AUTHOR), Li, Hongru1 (AUTHOR), Luo, Shengjie1 (AUTHOR)
Source: Journal of Computational Methods in Sciences & Engineering (Sage Publications Inc.). Mar2025, Vol. 25 Issue 2, p1114-1122. 9p.
Subjects: Matrix exponential, Exponential functions, Tikhonov regularization
Abstract: Tikhonov regularization is one of the most popular methods for solving linear discrete ill-posed problems. This approach involves transforming the original problem into a penalized least-squares problem, yielding a solution that exhibits greater robustness against data inaccuracies and computational errors that may occur during the solving process. The choice of the regularization matrix significantly influences the accuracy of the resulting solution. In this paper, we propose a novel method for selecting the regularization matrix based on exponential filter functions, which have a unique connection with Tikhonov filter functions. Our proposed Tikhonov-exponential regularization method only requires one parameter, similar to the traditional Tikhonov regularization method. Computational examples demonstrate the advantages of our proposed method. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational Methods in Sciences & Engineering (Sage Publications Inc.) is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
Text:
  Availability: 1
Header DbId: egs
DbLabel: Engineering Source
An: 184672180
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: An improved Tikhonov regularization method combined with the exponential filter function.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Zeng%2C+Xiaoniu%22">Zeng, Xiaoniu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xiaoniuzeng@163.com</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Tianyou%22">Liu, Tianyou</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tan%2C+Xiaofeng%22">Tan, Xiaofeng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Hongru%22">Li, Hongru</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Luo%2C+Shengjie%22">Luo, Shengjie</searchLink><relatesTo>1</relatesTo> (AUTHOR)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Methods+in+Sciences+%26+Engineering+%28Sage+Publications+Inc%2E%29%22">Journal of Computational Methods in Sciences & Engineering (Sage Publications Inc.)</searchLink>. Mar2025, Vol. 25 Issue 2, p1114-1122. 9p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Matrix+exponential%22">Matrix exponential</searchLink><br /><searchLink fieldCode="DE" term="%22Exponential+functions%22">Exponential functions</searchLink><br /><searchLink fieldCode="DE" term="%22Tikhonov+regularization%22">Tikhonov regularization</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Tikhonov regularization is one of the most popular methods for solving linear discrete ill-posed problems. This approach involves transforming the original problem into a penalized least-squares problem, yielding a solution that exhibits greater robustness against data inaccuracies and computational errors that may occur during the solving process. The choice of the regularization matrix significantly influences the accuracy of the resulting solution. In this paper, we propose a novel method for selecting the regularization matrix based on exponential filter functions, which have a unique connection with Tikhonov filter functions. Our proposed Tikhonov-exponential regularization method only requires one parameter, similar to the traditional Tikhonov regularization method. Computational examples demonstrate the advantages of our proposed method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Computational Methods in Sciences & Engineering (Sage Publications Inc.) is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=184672180
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1177/14727978241295283
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 9
        StartPage: 1114
    Subjects:
      – SubjectFull: Matrix exponential
        Type: general
      – SubjectFull: Exponential functions
        Type: general
      – SubjectFull: Tikhonov regularization
        Type: general
    Titles:
      – TitleFull: An improved Tikhonov regularization method combined with the exponential filter function.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Zeng, Xiaoniu
      – PersonEntity:
          Name:
            NameFull: Liu, Tianyou
      – PersonEntity:
          Name:
            NameFull: Tan, Xiaofeng
      – PersonEntity:
          Name:
            NameFull: Li, Hongru
      – PersonEntity:
          Name:
            NameFull: Luo, Shengjie
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 03
              Text: Mar2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 14727978
          Numbering:
            – Type: volume
              Value: 25
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: Journal of Computational Methods in Sciences & Engineering (Sage Publications Inc.)
              Type: main
ResultId 1