Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: Fabiana Zama
Pages: [145] - [167]
Received Date: October 8, 2009
Submitted by:
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 [2] test problems, and the results confirm the effectiveness and robustness of the method proposed.
singular value decomposition, regularization methods, Tikhonov method, ill-posed problems, integral equations.
