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Some error estimates for the reproducing kernel Hilbert spaces method.

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Title: Some error estimates for the reproducing kernel Hilbert spaces method.
Authors: Abbasbandy, Saeid1 abbasbandy@yahoo.com, Azarnavid, Babak2
Source: Journal of Computational & Applied Mathematics. Apr2016, Vol. 296, p789-797. 9p.
Subjects: Error analysis in mathematics, Estimation theory, Kernel (Mathematics), Hilbert space, Set theory, Boundary value problems, Mathematical bounds
Abstract: In this paper we derive some effective error estimates for the reproducing kernel Hilbert space method applied to a general class of linear initial or boundary value problems. The first error estimate is computable and yields a worst case bound in the form of a percentage of the norm of the true solution which has not yet been discussed according to the knowledge of the authors. The second error estimate is a residual based error estimate, which is expressed in terms of the fill distance, so that convergence is studied for the fill distance tends to zero. This is a generalization and improvement of the existing error estimates. Some numerical results are presented to demonstrate the applicability of the estimates. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. 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
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DbLabel: Engineering Source
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PubType: Academic Journal
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  Data: <searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Estimation+theory%22">Estimation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Kernel+%28Mathematics%29%22">Kernel (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Set+theory%22">Set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+bounds%22">Mathematical bounds</searchLink>
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  Data: In this paper we derive some effective error estimates for the reproducing kernel Hilbert space method applied to a general class of linear initial or boundary value problems. The first error estimate is computable and yields a worst case bound in the form of a percentage of the norm of the true solution which has not yet been discussed according to the knowledge of the authors. The second error estimate is a residual based error estimate, which is expressed in terms of the fill distance, so that convergence is studied for the fill distance tends to zero. This is a generalization and improvement of the existing error estimates. Some numerical results are presented to demonstrate the applicability of the estimates. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. 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.)
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      – Type: doi
        Value: 10.1016/j.cam.2015.10.035
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      – Code: eng
        Text: English
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        PageCount: 9
        StartPage: 789
    Subjects:
      – SubjectFull: Error analysis in mathematics
        Type: general
      – SubjectFull: Estimation theory
        Type: general
      – SubjectFull: Kernel (Mathematics)
        Type: general
      – SubjectFull: Hilbert space
        Type: general
      – SubjectFull: Set theory
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Mathematical bounds
        Type: general
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      – TitleFull: Some error estimates for the reproducing kernel Hilbert spaces method.
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              Text: Apr2016
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              Y: 2016
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              Value: 296
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