Fachbereich 6 Mathematik/Informatik

Institut für Informatik


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Masterseminar Exact Computation

6.666

Dozenten

Beschreibung

When designing new algorithms, in particular algorithms that involve a lot of computations and calculations, we typically think in the real numbers. Proofs about the correctness of algorithms are often carried out under the assumption of everything happening in the real numbers as well.

When then moving on to actually implement the algorithm, commonly one simply uses, e.g., "float" or "double" to represent the numbers the algorithm deals with, without much further thought about the fact that there certainly is some difference between real numbers and standard floating point numbers. "Maybe there is some tiny difference in the 15th decimal digit or so; who cares?"

Well, in various fields, for instance in graphical and geometric algorithms, there are common situations where it does not even matter how tiny the error is; even the tiniest inaccuracy can have catastrophic consequences, leading into, e.g., infinite loops or to invalid output (not just inaccurate, but structurally broken). Already something conceptually very simple, such as computing the intersection of two triangles, turns out to be a major challenge in the face of numerical inaccuracies - at least when things shall be implemented in a reliable manner, as expected and necessary in many industrial contexts.

In this seminar we will consider the question of how calculations can be carried out in standard digital computers without these issues; without the limited precision of floating point numbers breaking our assumptions. We will look at a number of techniques that allows us to actually perform >exact< computations in a computer, so as to preclude such issues. Alternatively, there are techniques, to the benefit of efficiency, to compute inexactly but >consistently<.

Key scenarios for such techniques can be found in the fields of geometric data processing, engineering, and graphics, but their utility extends to further fields and topics as well.

Weitere Angaben

Ort: (BBB-Meeting. Weitere Termine werden wir gemeinsam abstimmen.)
Zeiten: Termine am Dienstag. 13.04.21 15:00 - 16:00, Mittwoch. 21.04.21, Mittwoch. 12.05.21, Mittwoch. 19.05.21, Mittwoch. 26.05.21, Mittwoch. 02.06.21, Mittwoch. 09.06.21, Mittwoch. 16.06.21, Mittwoch. 23.06.21 17:00 - 19:00, Montag. 09.08.21 09:30 - 11:00, Montag. 09.08.21 11:15 - 12:45, Montag. 09.08.21 14:00 - 15:30, Montag. 09.08.21 15:45 - 17:15, Donnerstag. 12.08.21 09:30 - 11:00, Donnerstag. 12.08.21 11:15 - 12:45, Donnerstag. 12.08.21 14:00 - 15:30
Erster Termin: Di., 13.04.2021 15:00 - 16:00, Ort: (BBB-Meeting. Weitere Termine werden wir gemeinsam abstimmen.)
Veranstaltungsart: Seminar (Offizielle Lehrveranstaltungen)

Studienbereiche

  • Informatik > Master of Science in Informatik
  • Informatik > Master of Science in Informatik (bis PO 2016)
  • Informatik > Seminare
  • Mathematics/Computer Science