WIAS Preprint No. 959, (2004)

Degree of ill-posedness of statistical inverse problems



Authors

  • Mathé, Peter
    ORCID: 0000-0002-1208-1421

2010 Mathematics Subject Classification

  • 65J20 62G20

Keywords

  • Degree of ill--posedness, statistical inverse problem, variable Hilbert scale

Abstract

We introduce the notion of the degree of ill--posedness of linear operators in operator equations between Hilbert spaces. For specific assumptions on the noise this quantity can be computed explicitely. Next it is shown that the degree of ill--posedness as introduced explains the loss of accuracy when solving inverse problems in Hilbert spaces for a variety of instances.

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