Weighted and controlled frames
given at strobl07 (18.06.07 10:45)
Weighted and controlled frames have been introduced recently to improve the numerical efficiency of
iterative algorithms for inverting the frame operator. In this talk we develop systematically these notions including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition. We investigate the numerical advantages of introducing these concepts in the sense of preconditioning. We consider the special case of semi-normalized weights, where the concepts of weighted frames and standard frames are interchangeable. We also make the connection with frame multipliers.