Tikhonov-regularization of ill-posed linear operator equations on closed convex sets (Q1122727)

Convergence rates for an algorithm are proven. Let T map a real Hilbert space X linearly onto Y also a real Hilbert space. Let C be a closed convex subset of X. The algorithm is to find, for each positive a, the minimizing element in C of \(\| Tx-y\|^ 2+a\| x\|^ 2\). The paper presents conditions sufficient for the convergence of these minimizing elements (as a approaches 0) to the best approximate solution in C to \(Tx=y\). Under natural conditions, that involve the location of the metric and orthogonal projections of y, rates of convergence are given.