We show that the parallel projection method with variable weights and one variable relaxation coefficient for obtaining a point in the intersection of a finite number of closed convex sets in a given Hubert space may be interpreted as a semi-alternating sequential projection method in a suitably newly constructed Hubert space. As such, convergence results for the parallel projection method may ...

We formulate a solution to the diffuse optical tomography (DOT) inverse problem as the minimization of an energy functional of the solution and the data. For the solution prior we introduce a local diffusion regularization potential with a threshold based on robust statistics (the Hubert function). We compare results on simulated data for the Hubert function and two other standard regularizatio...

Dr. Jörg Lübcke has been the managing director of Burda Digital GmbH since 2010. The business area Digital of Hubert Burda Media combines the strategic Internet activities of the Group. It includes e-commerce companies andmarketing platforms, as well as companies in direct marketing, customer management, referral platforms as well as social media and corporate venture investments. The share of ...

We introduce a new method for computing the Hubert transform on the real line. It is a collocation method, based on an expansion in rational eigenfunctions of the Hubert transform operator, and implemented through the Fast Fourier Transform. An error analysis is given, and convergence rates for some simple classes of functions are established. Numerical tests indicate that the method compares f...

Equivalent conditions are given for the regularity of a factorization of a contraction, two of which exhibit immediately the duality property of this notion. The concept of regular factorization of contractions of Hubert spaces1 was introduced in [1] by the authors in connection with their investigations on the invariant subspace problem; cf. [2, §VIL3]. Let A0 be a contraction of a Hubert spac...

There are two important connections between the classes of nonexpansive and of accretive mappings which give rise to a strong connection between the fixed point theory of nonexpansive mappings and the mapping theory of accretive maps. These are: (1) If U is a nonexpansive mapping of D(U) into X, and if we set T — I--U, D(T)=D(U), then T is an accretive mapping of D{T) into X. (2) If { U(i)f t^O...