In this work‎, ‎an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$‎ ‎and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$‎ ‎where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎, ‎$ma...

Stephan Dahlke a, Massimo Fornasier b and Thorsten Raasch a a Philipps-Universität Marburg, FB 12 Mathematik und Informatik, Hans-Meerwein Straße, Lahnberge, 35032 Marburg, Germany E-mail: {dahlke;raasch}@mathematik.uni-marburg.de b Università “La Sapienza” in Roma, Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Via Antonio Scarpa, 16/B, 00161 Roma, Italy E-mail: mfornasi...

FP (g) = trgKerP − trgCokerP ∈ R(S) where R(S1) is the character ring of the S1-modules. We say that P is rigid with respect to this S1-action, if FP (g) is independent of g. Two well-known examples of rigid elliptic operators are the signature operator ds and the Dirac operator D [AH]. Now let L̃Spin(2l) denote the central extension of the loop group LSpin(2l) and E be a positive energy represe...

In structural design of steel frames, in order to achieve proper safety, the effect uncertainties and loading parameters structure must be considered. This approach is obtained by defining a reliability index. this study, Modified Dolphin Monitoring (MDM) operator was used evaluate index three well-known frame structures based on Hasofer-Lind method. The evaluated using EVPS VPS algorithms with...

We consider systems of vectors of the form {Ahi : i ∈ I, n ≥ 0} where {hi}i∈I is a countable (finite or infinite) system of vectors in a separable Hilbert space H and A ∈ B(H) is a bounded operator. We show that a system of that form can never be both complete and minimal, and find conditions that the operator A needs to satisfy for the system to be a frame or a complete Bessel system. We also ...