Regularized Ritz approximations for Fredholm equations of the first kind (Q1079924)

Suppose \(K: H_ 1\to H_ 2\) to be a compact linear operator not of finite rank, \(H_ 1\) and \(H_ 2\) Hilbert spaces. The problem is to find regularized approximations (in finite-dimensional subspaces \(V_ m)\) \(x_ m^{\delta}(\alpha)\) to the equation \(Kx=g\), \(g\in R(K)\), solution meaning ''minimal norm solution''. g is known approximately: \(\| g- g^{\delta}\| \leq \delta\), and \(\alpha\) is the parameter of Tikhonov regularization. The authors thoroughly discuss relations between \(\alpha\), \(\delta\) and \(\gamma_ m\) (the degree to which the subspace \(V_ m\) supports the operator K) with respect to weak or strong convergence of \(x_ m^{\delta}\) to x and to orders of convergence.