TY - CONF
AB - Do the solutions of linear equations depend computably on their coefficients? Implicitly, this has been one of the central questions in linear algebra since the very beginning of the subject and the famous Gauß algorithm is one of its numerical answers. Today there exists a tremendous number of algorithms which solve this problem for different types of linear equations. However, actual implementations in floating point arithmetic keep exhibiting numerical instabilities for ill-conditioned inputs. This situation raises the question which of these instabilities are intrinsic, thus caused by the very nature of the problem, and which are just side effects of specific algorithms. To approach this principle question we revisit linear equations from the rigorous point of view of computability. Therefore we apply methods of computable analysis, which is the Turing machine based theory of computable real number functions. It turns out that, given the coefficients of a system of linear equations, we can compute the space of solutions, if and only if the dimension of the solution space is known in advance. Especially, this explains why there cannot exist any stable algorithms under weaker assumptions.
AU - Brattka, Vasco
AU - Ziegler, Martin
ID - 18179
T2 - Proceedings of the 2nd IFIP International Conference on Theoretical Computer Science
TI - Computability of Linear Equations
ER -
TY - CONF
AB - We present a new data structure for rendering highly complex virtual environments of arbitrary topology. The special feature of our approach is that it allows an interactive navigation in very large scenes (30 GB/400 million polygons in our benchmark scenes) that cannot be stored in main memory, but only on a local or remote hard disk. Furthermore, it allows interactive rendering of substantially more complex scenes by instantiating objects.
For the computation of an approximate image of the scene, a sampling technique is used. In the preprocessing, a so-called sample tree is built whose nodes contain randomly selected polygons from the scene. This tree only uses space that is linear in the number of polygons. In order to produce an image of the scene, the tree is traversed and polygons stored in the visited nodes are rendered. During the interactive walkthrough, parts of the sample tree are loaded from local or remote hard disk.
We implemented our algorithm in a prototypical walkthrough system. Analysis and experiments show that the quality of our images is comparable to images computed by the conventional z-buffer algorithm regardless of the scene topology.
AU - Klein, Jan
AU - Krokowski, Jens
AU - Fischer, Matthias
AU - Wand, Michael
AU - Wanka, Rolf
AU - Meyer auf der Heide, Friedhelm
ID - 16490
SN - 1581135300
T2 - Proceedings of the ACM symposium on Virtual reality software and technology - VRST '02
TI - The randomized sample tree: a data structure for interactive walkthroughs in externally stored virtual environments
ER -
TY - CONF
AB - Visualising is a method used to help experiencing and understanding causal cohesions in simulation processes. For this purpose, tools for visualising are already implemented in prevalent simulation systems. The user creates his simulation model and generates a 3-dimensional (2,5-dimensional) visualising by means of the simulation system. This helps examining the process which makes it easier for the viewer to understand it. Simulation tools usually only provide the opportunity for a unidirectional visualising. In a 3-dimensional surrounding the viewer can not implement an interaction with the simulation while the system is running. Though an interaction during the simulation run enables the user to gain a better understanding of causal cohesions. Solutions via HLA are sophisticated and therefore rather suited for extensive projects.
We present a distributed system consisting of a commercial manufacturing simulation tool, a coupling module and a walkthrough system. The distributed system in conjunctions with the coupling module guarantees generality and a wide field of applications of the walkthrough system. Further it guarantees flexibility and selection of the specialized graphics hardware for the walkthrough system. A further contribution of this paper is the solution of the time synchronisation problem caused by simulation tool and walkthrough system.
AU - Mueck, Bengt
AU - Dangelmaier, Wilhelm
AU - Fischer, Matthias
AU - Klemisch, Wolfram
ID - 18369
T2 - Simulation und Visualisierung
TI - Bi-directional Coupling of Simulation Tools with a Walkthrough-System
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18408
T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 0987.00002]
TI - Waldegg, Guillermina, “Ontological Convictions and Epistemological Obstacles in Bolzano’s Geometry”, Science and Education 10 (2001), 409–418
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18403
T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 0981.03004]
TI - Linsky, Bernard, Russell’s Metaphysical Logic, CSLI Publications: Stanford, CA 1999
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18410
T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 0990.03002]
TI - Moore, Gregory H., “The Prehistory of Infinitary Logic: 1885–1955”, in: Maria Luisa Dalla Chiara u.a. (Hgg.), Structures and Norms in Science. Volume two of the 10th International Congress of Logic, Methodology and Philosophy of Science, Florence, Italy, August 1995, Dordrecht: Kluwer Academic Publishers 1997, 105–123
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18415
T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 0993.01003, Reprint von MR 2002h:01005]
TI - Degnan, Michael J., “What is the Scope of Aristotle’s Defense of the PNC”, Apeiron 32 (1999), no. 3, 243–274
ER -
TY - CHAP
AU - Tophinke, Doris
ED - Bommes, Michael
ED - Noack, Christina
ED - Tophinke, Doris
ID - 18287
T2 - Sprache als Form. FS für Utz Maas
TI - Schreiben gegen die Regel – Formen und Funktionen orthografischer Abweichungen im Internet Relay Chat (IRC)
ER -
TY - CHAP
AU - Tophinke, Doris
ED - Drescher, Martina
ID - 18321
T2 - Textsorten im romanischen Sprachvergleich
TI - Texttypologie aus diachroner Sicht
ER -
TY - CONF
AB - We analyze a randomized pursuit-evasion game on graphs. This game is played by two players, a hunter and a rabbit. Let G be any connected, undirected graph with n nodes. The game is played in rounds and in each round both the hunter and the rabbit are located at a node of the graph. Between rounds both the hunter and the rabbit can stay at the current node or move to another node. The hunter is assumed to be restricted to the graph G: in every round, the hunter can move using at most one edge. For the rabbit we investigate two models: in one model the rabbit is restricted to the same graph as the hunter, and in the other model the rabbit is unrestricted, i.e., it can jump to an arbitrary node in every round.
We say that the rabbit is caught as soon as hunter and rabbit are located at the same node in a round. The goal of the hunter is to catch the rabbit in as few rounds as possible, whereas the rabbit aims to maximize the number of rounds until it is caught. Given a randomized hunter strategy for G, the escape length for that strategy is the worst case expected number of rounds it takes the hunter to catch the rabbit, where the worst case is with regards to all (possibly randomized) rabbit strategies. Our main result is a hunter strategy for general graphs with an escape length of only O
(n log (diam(G))) against restricted as well as unrestricted rabbits. This bound is close to optimal since Ω(n) is a trivial lower bound on the escape length in both models. Furthermore, we prove that our upper bound is optimal up to constant factors against unrestricted rabbits.
AU - Adler, Micah
AU - Räcke, Harald
AU - Sivadasan, Naveen
AU - Sohler, Christian
AU - Vöcking, Berthold
ID - 18566
SN - 0302-9743
T2 - Proceedings of the 29th International Colloquium on Automata, Languages and Programming
TI - Randomized Pursuit-Evasion in Graphs
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18756
T2 - Mathematical Reviews [MR 2002h:01005]
TI - Degnan, Michael J., “What is the Scope of Aristotle’s Defense of the PNC”, Apeiron 32 (1999), no. 3, 243–274
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18751
T2 - Mathematical Reviews [MR 2002h:01001]
TI - Thom, Paul, “The Principle of Non-contradiction in Early Greek Philosophy”, Apeiron 32 (1999), no. 3, 153–170
ER -
TY - JOUR
AU - Eke, Norbert Otto
ID - 19362
IS - Juli
JF - Text + Kritik, H. 155: Herta Müller
TI - Schönheit der Verwund(er)ung. Herta Müllers Weg zum Gedicht
ER -
TY - THES
AU - Sohler, Christian
ID - 18573
SN - 3-935433-28-X
TI - Property Testing and Geometry
ER -
TY - CONF
AU - Wanka, Rolf
ID - 19850
SN - 0302-9743
T2 - Proc. Workshop on Graph-Theoretic Concepts in Computer Science (WG)
TI - Any Load-Balancing Regimen for Evolving Tree Computations on Circulant Graphs Is Asymptotically Optimal
ER -
TY - CONF
AU - Brinkmann, André
AU - Salzwedel, Kay
AU - Scheideler, Christian
ID - 2136
T2 - SPAA
TI - Compact, adaptive placement schemes for non-uniform requirements
ER -
TY - JOUR
AU - de los Arcos, T.
AU - Vonau, F.
AU - Garnier, M. G.
AU - Thommen, V.
AU - Boyen, H.-G.
AU - Oelhafen, P.
AU - Düggelin, M.
AU - Mathis, D.
AU - Guggenheim, R.
ID - 22620
JF - Applied Physics Letters
SN - 0003-6951
TI - Influence of iron–silicon interaction on the growth of carbon nanotubes produced by chemical vapor deposition
ER -
TY - JOUR
AU - Fischer, Gerd
AU - Heyken, Reent
AU - Trächtler, Ansgar
ID - 23344
JF - ATZ Worldwide 104
TI - Active stabilisation of the car-trailer combination with BMW X5 An innovative further improvement of the dynamic stability control DSC for active damping of trailer sway movements
ER -
TY - THES
AU - Goldschmidt, Stefan
ID - 24599
TI - Anwendung mengenorientierter numerischer Methoden zur Analyse nichtlinearer dynamischer Systeme am Beispiel der Spurführungsdynamik von Schienenfahrzeugen
VL - 112
ER -
TY - GEN
ED - Gausemeier, Jürgen
ID - 24594
TI - 1. Paderborner Workshop Augmented & Virtual Reality in der Produktentstehung
VL - 107
ER -