Regularization by projection in variable Hilbert scales

References

• Engl , HW , Hanke , M and Neubauer , A . 1996 . Regularization of Inverse Problems, Mathematics and its Applications , Vol. 375 , Dordrecht : Kluwer Academic Publishers Group .
   Google Scholar
• Natterer , F . 1977 . Regularisierung schlecht gestellter Probleme durch Projektionsverfahren . Numerische Mathematik , 28 ( 3 ) : 329 – 341 .
   Web of Science ®Google Scholar
• Vaǐnikko , GM and Khyamarik , UA . 1985 . Projection methods and self-regularization in ill-posed problems . Izvestiya Vysshikh Uchebnykh Zavedenii Matematika , 84 ( 10 ) : 3 – 17 .
   Google Scholar
• Mathé , P and Pereverzev , SV . 2003 . Discretization strategy for linear ill-posed problems in variable Hilbert scales . Inverse Problems , 19 ( 6 ) : 1263 – 1277 .
   Web of Science ®Google Scholar
• Mathé , P and Pereverzev , SV . 2003 . Geometry of linear ill-posed problems in variable Hilbert scales . Inverse Problems , 19 ( 3 ) : 789 – 803 .
   Web of Science ®Google Scholar
• Nair , MT , Pereverzev , SV and Tautenhahn , U . 2005 . Regularization in Hilbert scales under general smoothing conditions . Inverse Problems , 21 ( 6 ) : 1851 – 1869 .
   Web of Science ®Google Scholar
• Kaltenbacher , B . 2000 . Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems . Inverse Problems , 16 ( 5 ) : 1523 – 1539 .
   Web of Science ®Google Scholar
• Hofmann , B and Fleischer , G . 1999 . Stability rates for linear ill-posed problems with compact and non-compact operators . Zeitschrift fur Analysis und ihre Anwendungen , 18 ( 2 ) : 267 – 286 .
   Google Scholar
• Pietsch , A . 1980 . Operator Ideals , Amsterdam : North-Holland Publishing Co. . (Translated from German by the author)
   Google Scholar
• Hofmann , B and Yamamoto , M . 2005 . Convergence rates for Tikhonov regularization based on range inclusions . Inverse Problems , 21 ( 3 ) : 805 – 820 .
   Web of Science ®Google Scholar
• Hofmann , B and Mathé , P . 2007 . Analysis of profile functions for general linear regularization methods . SIAM Journal of Numerical Analysis , 45 ( 3 ) : 1122 – 1141 . (electronic)
   Web of Science ®Google Scholar
• Mathé , P and Pereverzev , SV . 2001 . Optimal discretization of inverse problems in Hilbert scales. Regularization and self-regularization of projection methods . SIAM Journal of Numerical Analysis , 38 ( 6 ) : 1999 – 2021 .
   Google Scholar
• Mathé , P and Hofmann , B . 2006 . Direct and Inverse Results in Variable Hilbert Scales , Chemnitz : TU . preprint 2006-27, to appear J. Approx. Theory, 2008
   Google Scholar
• Hofmann , B , Mathé , P and Pereverzev , SV . 2007 . Regularization by projection: approximation theoretic aspects and distance functions . Journal of Inverse Ill-Posed Problems , 15 ( 5 ) : 527 – 545 .
   Google Scholar
• Adams , RA . 1975 . Sobolev Spaces, Pure and Applied Mathematics , Vol. 65 , New York-London : Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers] .
   Google Scholar
• Kirsch , A . 1996 . “ An Introduction to the Mathematical Theory of Inverse Problems, Applied Mathematical Sciences ” . Vol. 120 , New York : Springer-Verlag .
   Google Scholar
• Böttcher , A . 2006 . Convergence rates for Tikhonov regularization from different kinds of smoothness conditions . Applied Analysis , 85 ( 5 ) : 555 – 578 .
   Google Scholar
• Mathé , P and Tautenhahn , U . 2006 . Interpolation in variable Hilbert scales with application to inverse problems . Inverse Problems , 22 ( 6 ) : 2271 – 2297 .
   Google Scholar
• Mathé , P and Pereverzev , SV . 2006 . The discretized discrepancy principle under general source conditions . Journal of Complexity , 22 ( 3 ) : 371 – 381 .
   Web of Science ®Google Scholar
• Mathé , P . 2006 . The Lepskiǐ principle revisited . Inverse Problems , 22 ( 3 ) : L11 – L15 .
   Web of Science ®Google Scholar
• Mathé , P . 2006 . What do we learn from the discrepancy principle? . Zeitschrift fur Analysis und ihre Anwendungen , 25 ( 4 ) : 411 – 420 .
   Google Scholar
• Schock , E . 1986 . What are the proper condition numbers of discretized ill-posed problems? . Linear Algebra and its Applications , 81 : 129 – 136 .
   Google Scholar