253 IGPM253.pdf        October 2005
TITLE Error Controlled Regularization by Projection
AUTHORS Wolfgang Dahmen, Markus Jürgens
ABSTRACT The paper is concerned with regularization concepts for the inversion of diffusion processes. The application of the involved evolution operators is based on Dunford integral representations combined with the adaptive application of resolvents using recent wavelet methods. In particular, this allows us to develop and realize numerically, to our knowledge for the first time in this context, an SVD projection method which is compared to several versions of Tikhonov-type schemes. The theoretical findings are complemented by numerical tests shedding some light on the quantitative performance of the schemes.
KEYWORDS inverse problems, Dunford integrals, quadrature, Tikhonov method, projection methods, truncated SVD expansion, adaptive wavelet methods
PUBLICATION Electronic transactions on numerical analysis : ETNA
25, 67-100 (2006)