Oblique projections, pseudoinverses, and standard-form transformations

Per Christian Hansen

AbstractStandard-form transformation is a technique for transforming a discrete ill-posed problem in general form (with a seminorm as regularizing term) into a standard-form problem. We give a simple geometric explanation why the weighted pseudoinverse is the correct inverse to use in the standard-form transformation. Our presentation is based on oblique projections and oblique pseudoinverses - tools that are often overlooked in numerical analysis.
KeywordsOblique projection, oblique pseudoinverse, weighted pseudoinverse
TypeTechnical report
PublisherInformatics and Mathematical Modelling, Technical University of Denmark, DTU
AddressRichard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby
SeriesIMM-Technical report- 2004-13
BibTeX data [bibtex]
IMM Group(s)Scientific Computing