Arnoldi-Tikhonov regularization methods
نویسندگان
چکیده
Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining a partial Lanczos bidiagonalization of the matrix of the given system of equations. This paper explores the possibility of instead computing a partial Arnoldi decomposition of the given matrix. Computed examples illustrate that this approach may require fewer matrix-vector product evaluations and, therefore, less arithmetic work. Moreover, the proposed range-restricted ArnoldiTikhonov regularization method does not require the adjoint matrix and, hence, is convenient to use for problems for which the adjoint is difficult to evaluate.
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