Abstract
Discrete ill-posed problems are difficult to solve, because their solution is very sensitive to errors in the data and to round-off errors introduced during the solution process. Tikhonov regularization replaces the given discrete ill-posed problem by a nearby penalized least-squares problem whose solution is less sensitive to perturbations. The penalization term is defined by a regularization matrix, whose choice may affect the quality of the computed solution significantly. We describe several inverse matrix problems whose solution yields regularization matrices adapted to the desired solution. Numerical examples illustrate the performance of the regularization matrices determined.
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Dedicated to Claude Brezinski and Sebastiano Seatzu on the Occasion of Their 70th Birthdays.
Research of S. Noschese was supported by a grant from SAPIENZA Università di Roma.
Research of L. Reichel was supported in part by NSF grant DMS-1115385.
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Noschese, S., Reichel, L. Inverse problems for regularization matrices. Numer Algor 60, 531–544 (2012). https://doi.org/10.1007/s11075-012-9576-8
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DOI: https://doi.org/10.1007/s11075-012-9576-8