## Finite-dimensional approximation of constrained Tikhonov-regularized solutions of ill-posed linear operator equations

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## Abstract:

In this paper we derive conditions under which the finite-dimensional constrained Tikhonov-regularized solutions ${x_{\alpha ,{C_n}}}$ of an ill-posed linear operator equation $Tx = y$ (i.e., ${x_{\alpha ,{C_n}}}$ is the minimizing element of the functional ${\left \| {Tx - y} \right \|^2} + \alpha {\left \| x \right \|^2}$, $\alpha > 0$ in the closed convex set ${C_n}$, which is a finite-dimensional approximation of a closed convex set*C*) converge to the best approximate solution of the equation in

*C*. Moreover, we develop an estimate for the approximation error, which is optimal for certain sets

*C*and ${C_n}$. We present numerical results that verify the theoretical results.

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## Additional Information

- © Copyright 1987 American Mathematical Society
- Journal: Math. Comp.
**48**(1987), 565-583 - MSC: Primary 65J10; Secondary 65R20
- DOI: https://doi.org/10.1090/S0025-5718-1987-0878691-2
- MathSciNet review: 878691