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In this paper we derive conditions under which the finite-dimensional constrained Tikhonov-regularized solutions x, c of an ill-posed linear operator equation Tx = y (i.e., Xac is the minimizing element of the functional IITx - y112 + alIx112, a > 0 in the closed convex set C,?, 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,?. We present numerical results that verify the theoretical results.

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