TY - JOUR
AU - Dellnitz, Michael
AU - Junge, Oliver
AU - Thiere, Bianca
ID - 17027
IS - 1531-3492_2001_1_125
JF - Discrete & Continuous Dynamical Systems - B
SN - 1531-3492
TI - The numerical detection of connecting orbits
VL - 1
ER -
TY - CHAP
AU - Froyland, Gary
ID - 16598
SN - 9781461266488
T2 - Nonlinear Dynamics and Statistics
TI - Extracting Dynamical Behavior via Markov Models
ER -
TY - JOUR
AU - Froyland, Gary
AU - Junge, Oliver
AU - Ochs, Gunter
ID - 16601
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
TI - Rigorous computation of topological entropy with respect to a finite partition
ER -
TY - CHAP
AU - Dellnitz, Michael
AU - Froyland, Gary
AU - Junge, Oliver
ID - 16555
SN - 9783642625244
T2 - Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems
TI - The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems
ER -
TY - CONF
AB - Computing the spectral decomposition of a normal matrix is among the most frequent tasks to numerical mathematics. A vast range of methods are employed to do so, but all of them suffer from instabilities when applied to degenerate matrices, i.e., those having multiple eigenvalues. We investigate the spectral representation's effectivity properties on the sound formal basis of computable analysis. It turns out that in general the eigenvectors cannot be computed from a given matrix. If however the size of the matrix' spectrum (=number of different eigenvalues) is known in advance, it can be diagonalized effectively. Thus, in principle the spectral decomposition can be computed under remarkably weak non-degeneracy conditions.
AU - Ziegler, Martin
AU - Brattka, Vasco
ID - 18152
SN - 0302-9743
T2 - Proceedings of the 4th Workshop on Computability and Complexity in Analysis (CCA'2000)
TI - A Computable Spectral Theorem
VL - 2064
ER -
TY - CONF
AB - We present a new output-sensitive rendering algorithm, the randomized z-buffer algorithm. It renders an image of an arbitrary three-dimensional scene consisting of triangular primitives by reconstruction from a dynamically chosen set of random surface sample points. This approach is independent of mesh connectivity and topology. The resulting rendering time grows only logarithmically with the numbers of triangles in the scene. We were able to render walkthroughs of scenes of up to 10^14 triangles at interactive frame rates. Automatic identification of low detail scene components ensures that the rendering speed of the randomized z-buffer cannot drop below that of conventional z-buffer rendering. Experimental and analytical evidence is given that the image quality is comparable to that of common approaches like z-buffer rendering. The precomputed data structures employed by the randomized z-buffer allow for interactive dynamic updates of the scene. Their memory requirements grow only linearly with the number of triangles and allow for a scene graph based instantiation scheme to further reduce memory consumption.
AU - Wand, Michael
AU - Fischer, Matthias
AU - Peter, Ingmar
AU - Meyer auf der Heide, Friedhelm
AU - Straßer, Wolfgang
ID - 16492
SN - 158113374X
T2 - Proceedings of the 28th annual conference on Computer graphics and interactive techniques - SIGGRAPH '01
TI - The randomized z-buffer algorithm
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18378
T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 952.03068]
TI - Wehmeier, Kai F., “Consistent Fragments of Grundgesetze and the Existence of Non-logical Objects”, Synthese 121 (1999), 309–328
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18392
T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 970.03002]
TI - Pelletier, Francis Jeffry, “Did Frege Believe Frege’s Principle?”, Journal of Logic, Language, and Information 10 (2001), 87–114
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18380
T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 953.03005]
TI - Schirn, Matthias (Hg.), Frege: Importance and Legacy, Walter de Gruyter: Berlin 1996 (Perspectives in Analytical Philosophy; 13)
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18385
T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 961.01021]
TI - Casti, John L./DePauli, Werner, Gödel: A Life of Logic, Perseus Publishing: Cambridge, Mass. 2000
ER -