In much of the literature on the solution of linear ill-posed operator equations, the operator equation is discretized and regularization methods are developed for the discretized problem so obtained, without discussing the ramification of these methods for the infinite-dimensional problem. In particular, these regularization methods may only be applicable to certain linear ill-posed operator equations. This paper discusses how regularization by a modified truncated singular value decomposition introduced in [21] for finite-dimensional problems can be extended to operator equations. In finite dimensions, this regularization method yields approximate solutions of higher quality than standard truncated singular value decomposition. Our analysis in a Hilbert space setting is of practical interest, because the solution method presented avoids introduction of discretization errors during the solution process. We discuss how to construct such problems with Chebfun.

 

Zeitschrift:

Journal of Computational and Applied Mathematics

Seiten:

116621

Band:

467