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Sparse linear algebraic data structures are widely used during the solution of large scale linear optimization problems. The efficiency of the solver is significantly influenced by the used data structures. The implementations of such data structures are not trivial. A performance analysis of the available data structures can provide valuable information to improve efficiency. In the talk we present our software that supports this task as well as our new, special vector representation. We also report results covering the solution for numerical issues affecting the performance of sparse linear algebraic operations.

A Grid Data Structure The numbers of different grid entities, i.e. triangles, vertices, edges, and boundary edges are relevant in several aspects and hence are named consistently as shown in Table A.1: Table A.1. Notation for number of grid entities. grid entity vertices triangles edges boundary edges symbol 𝑛 𝑚 𝑠 𝑟 The grid is stored in a single Matlab structure. This structure has been extended in the course of the text, starting from vertices and triangles (Chapter 2.1), adding bound- ary edges (Chapter 2.4) and vertex levels (Chapter 6.3). The complete

Triangle Meshes. - Journal of Graphics Tools, Vol. 3, 1998, No 4, 1-11. 5. Weiler, K. Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments. - IEEE Computer Graphics and Applications, Vol. 5, 1985, No 1, 21-24. 6. Pulli, K., M. Segal. Fast Rendering of Subdivision Surfaces. - In: Proc. of the Eurographics Workshop on Rendering Techniques, Porto, Portugal, 1996, 61-70. 7. Ou, Shiqi, Hongzan Bin. A Compact Data Structure for Implementing Loop Subdivision. - International Journal of Advanced Manufacturing Technology, Vol. 29, 2006, No 11, 1151-1158. 8

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Russ. J. Numer. Anal. Math. Modelling, Vol. 18, No. 1, pp. 1–11 (2003) c° VSP 2003 Parallel multilevel data structures for a nonconforming Ž nite element problem on unstructured meshes V. CHUGUNOV¤ and Yu. VASSILEVSKI¤ Abstract — A parallel version of a multigrid method [5] for a face-oriented nonconforming Ž nite element space is considered. Primary attention is focused on a data structure providing simple imple- mentation. In particular, a technique of parallelization is derived in a logically consistent way from a set of a priori formulated requirements to the

Introduction Current novel positron emission tomography (PET) scanners [1–8] are complex devices built from hundreds of small scintillating detectors that register large amount of data that need to be handled and processed. For the J-PET project, a new framework was developed [9] to control data processing and reconstruction. Such framework can run in an environment that provides sufficient data capacity, read-write speed, and CPU power [10]. To optimize speed for both reconstruction code development and data analysis, new data structure and database were created

Data Structure for Flights and Walkthroughs in Urban Scenes with Mobile Elements. - Computer Graphics Forum, Vol. 29, 2010, No 6, pp. 1745-1755. 8. Ahn, H. K., N. Mamoulis, H. M. Wong. A Survey on Multidimensional Access Methods. 2001, pp. 1-19. 9. Gong Jun, Zhu Qing. An Adaptice Control Method of LODs for 3D Scene Based on R-Tree Index. - Acta Geodaetica et Cartographica Sinica, Vol. 40, 2011, No 4, pp. 531-534. 10. Chen Peng, Meng Lingkui. R-Tree Structure Appended with Spatial Topology Restrictions in 3D GIS. - Geomatics and Information Science of Wuhan University

Miguel Moscoso, Alexei Novikov, George Papanicolaou, and Chrysoula Tsogka Data structures for robust multifrequency imaging Abstract: In this paper, we consider imaging problems that can be cast in the form of an underdetermined linear system of equations. When a single measurement vec- tor is available, a sparsity promoting ℓ1-minimization-based algorithm may be used to solve the imaging problem efficiently. A suitable algorithm in the case of multiple measurement vectors would be the MUltiple SIgnal Classification (MUSIC) which is a subspace projection method