The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices include the identity matrix and finite difference approximations of a derivative operator. It is the purpose of the present paper to explore the use of fractional powers of the matrices A^TA (for Tikhonov regularization) and A (for Lavrentiev regularization) as regularization matrices, where A is the matrix that defines the linear discrete ill-posed problem. Both small and large-scale problems are considered.
Keywords: Ill-posed problem; fractional Tikhonov regularization; fractional Lavrentiev regularization; fractional power regularization matrix

Name | CASA-report |
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Volume | 1328 |
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ISSN (Print) | 0926-4507 |
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