A new wavelet method for solving an ill-posed problem
So far there are many papers which deal with the Cauchy problem for elliptic equation. However, most of them are devoted to the case of constant coefficients. In this paper, we consider a Cauchy problem for an elliptic equation with variable coefficients. Due to ill-posedness of this problem, we pro...
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| Vydané v: | Applied mathematics and computation Ročník 203; číslo 2; s. 635 - 640 |
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| Médium: | Journal Article |
| Jazyk: | English |
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New York, NY
Elsevier Inc
15.09.2008
Elsevier |
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | So far there are many papers which deal with the Cauchy problem for elliptic equation. However, most of them are devoted to the case of constant coefficients. In this paper, we consider a Cauchy problem for an elliptic equation with variable coefficients. Due to ill-posedness of this problem, we provide a regularization method – wavelet dual least squares method to solve the problem. Via Meyer wavelet bases with a special project method dual least squares method, we can obtain error estimate between the regularized solution and exact solution. |
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| AbstractList | So far there are many papers which deal with the Cauchy problem for elliptic equation. However, most of them are devoted to the case of constant coefficients. In this paper, we consider a Cauchy problem for an elliptic equation with variable coefficients. Due to ill-posedness of this problem, we provide a regularization method – wavelet dual least squares method to solve the problem. Via Meyer wavelet bases with a special project method dual least squares method, we can obtain error estimate between the regularized solution and exact solution. |
| Author | Qian, Ailin |
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| Keywords | Wavelet Inverse problems Elliptic equation Regularization Error estimate Error estimation Numerical linear algebra Partial differential equation Cauchy problem Inverse problem Exact solution Regularization method Wavelets Numerical analysis Wavelet transformation Applied mathematics Least squares method Ill posed problem |
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| SubjectTerms | Elliptic equation Error estimate Exact sciences and technology Fourier analysis Inverse problems Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Partial differential equations Regularization Sciences and techniques of general use Wavelet |
| Title | A new wavelet method for solving an ill-posed problem |
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