Projection Methods for Linear Equations in Hilbert Spaces

Projections and projection methods in abstract vector spaces show similarities and differences when compared to the finite-dimensional case. The difference stems from the change from finite- to infinite-dimensional vector spaces. Since a deeper study requires a strong background in functional analysis we restrict the subject to results that can be understood easily. We concentrate on the alternating projection method that is behind the many algorithms we studied in earlier chapters. For easier understanding we summarize the necessary basic concepts and results from functional analysis. For deeper details the reader can consult with any of the books [177], [6], [301], [236], [217], [113], [128], [27] and the references therein.