This paper investigates the linear feasibility problem (LFP), which plays a fundamental role in image reconstruction, especially in applications such as computed tomography and signal processing. The goal is to find a point in the intersection of a finite collection of convex sets defined by linear constraints. We provide a structured overview and comparison of existing ORTHOGONAL projection-based iterative methods for solving LFPs, including sequential, simultaneous, and block-iterative algorithms. While these methods have been studied individually in the literature, our work highlights their theoretical underpinnings, practical performance, and convergence properties in a unified framework. We also revisit and refine known convergence theorems, discussing their assumptions and implications in the context of real-world reconstruction problems. The novelty of this study lies in its comprehensive synthesis of algorithmic strategies along with a critical analysis of their relative strengths, limitations, and applicability. This work aims to clarify the landscape of projection methods for LFPs and to guide the selection or development of more effective reconstruction techniques in practice.

Let H be a complex Hilbert space. We study the geometry of the space of pairs (A, E), for A a (semidefinite bounded linear) positive operator on H and E a (bounded linear) projection on H such that AE=E*A.

In this paper, some fixed point results of self mapping which is defined on ORTHOGONAL cone metric spaces are given by using extensions of ORTHOGONAL contractions. And by taking advantage of these results, the necessary conditions for self mappings on ORTHOGONAL cone metric space to have P property are investigated. Also an example is given to illustrate the main results.

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We extend Jordan's notion of principal angles to work for two subspaces of quaternionic space, and so have a method to analyze two ORTHOGONAL PROJECTIONS in the matrices over the real, complex or quaternionic field (or skew field). From this we derive an algorithm to turn almost commuting PROJECTIONS into commuting PROJECTIONS that minimizes the sum of the displacements of the two PROJECTIONS. We quickly prove what we need using the universal real C*-algebra generated by two PROJECTIONS.

In this research, performance analysis for the composition of non-ORTHOGONAL and ORTHOGONAL cellular digital television broadcasting is investigated. A downlink multi-carrier layered division multiplexing (LDM) superimposed with an evolved multimedia broadcast multicast service (eMBMS). We define two broadcast service providers (BSP), which offer different radio access technology (RAT). The BER and Sum-Rate efficiency are selected as our criteria. The proposed downlink composition framework can work without a subscriber identity module (SIM card) uplink and internet protocol (IP). Mathematical analysis, based on the exact closed-form expressions, is consistent with the theory of the proposed composition LDM/eMBMS. Evaluation and performance are done based on the Monte Carlo iterative methodology. The results show that the BER and Sum-Rate performance of a composition framework outperforms compared with LDM/eMBMS individually system.

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