Zama, Fabiana
(2009)
Computation of Regularization Parameters using the Fourier Coefficients.
[Preprint]
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Abstract
In the solution of ill-posed problems by means of regularization
methods, a crucial issue is the computation of the regularization
parameter. In this work we focus on the Truncated Singular Value
Decomposition (TSVD) and Tikhonov method and we define a method for
computing the regularization parameter based on the behavior of
Fourier coefficients. We compute a safe index for truncating the
TSVD and consequently a value for the regularization parameter of
the Tikhonov method. An extensive numerical experimentation is
carried out on the Hansen's Regtool test problems and
the results confirm the effectiveness and robustness of the method
proposed.
Abstract
In the solution of ill-posed problems by means of regularization
methods, a crucial issue is the computation of the regularization
parameter. In this work we focus on the Truncated Singular Value
Decomposition (TSVD) and Tikhonov method and we define a method for
computing the regularization parameter based on the behavior of
Fourier coefficients. We compute a safe index for truncating the
TSVD and consequently a value for the regularization parameter of
the Tikhonov method. An extensive numerical experimentation is
carried out on the Hansen's Regtool test problems and
the results confirm the effectiveness and robustness of the method
proposed.
Document type
Preprint
Creators
Keywords
Singular Value Decomposition, Regularization methods, Tikhonov method,
Ill-posed problems, Integral equations
Subjects
DOI
Deposit date
18 Jun 2009
Last modified
16 May 2011 12:10
URI
Other metadata
Document type
Preprint
Creators
Keywords
Singular Value Decomposition, Regularization methods, Tikhonov method,
Ill-posed problems, Integral equations
Subjects
DOI
Deposit date
18 Jun 2009
Last modified
16 May 2011 12:10
URI
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