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Convergence rates of approximate least squares solutions of linear integral and operator equations of the first kind

1974
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Mathematics of Computation
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We consider approximations \xn] obtained by moment discretization to (i) the minimal £2-norm solution of Six = y where 3C is a Hilbert-Schmidt integral operator on £2, and to (ii) the least squares solution of minimal £2-norm of the same equation when y is not in the range 5i(X) of X. In case (i), if y £ X^y, where 3Cf is the generalized inverse of X. and ||a:"|| -> <» otherwise. Rates of convergence are given in this case if further X^y £ 3C*(£2), where X* is the adjoint of 3C, and the

doi:10.1090/s0025-5718-1974-0461895-1
fatcat:wccfvi3hh5eb7of2d6wcmqiz5y