Module Description

Module: Hierarchical Algorithms

Courses:

TitleTypeHrs/WeekPeriod
Hierarchical AlgorithmsLecture2Winter Semester
Hierarchical AlgorithmsRecitation Section (small)2Winter Semester

Module Responsibility:

Prof. Sabine Le Borne

Admission Requirements:

None

Recommended Previous Knowledge:

  • Mathematics I, II, III for Engineering students (german or english) or Analysis & Linear Algebra I + II as well as Analysis III for Technomathematicians
  • Programming experience in C

Educational Objectives:

Professional Competence

Theoretical Knowledge

Students are able to

  • name representatives of hierarchical algorithms and list their characteristics,
  • explain construction techniques for hierarchical algorithms,
  • discuss aspects regarding the efficient implementation of hierarchical algorithms.
Capabilities

Students are able to

  • implement the hierarchical algorithms discussed in the lecture,
  • analyse the storage and computational complexities of the algorithms,
  • adapt algorithms to problem settings of various applications and thus develop problem adapted variants.

Personal Competence

Social Competence

Students are able to

  • work together in heterogeneously composed teams (i.e., teams from different study programs and background knowledge), explain theoretical foundations and support each other with practical aspects regarding the implementation of algorithms.
Autonomy

Students are capable

  • to assess whether the supporting theoretical and practical excercises are better solved individually or in a team,
  • to work on complex problems over an extended period of time,
  • to assess their individual progess and, if necessary, to ask questions and seek help.

ECTS-Credit Points Module:

6 ECTS

Examination:

Oral exam

Workload in Hours:

Independent Study Time: 124, Study Time in Lecture: 56


Course: Hierarchical Algorithms

Lecturer:

Sabine Le Borne

Language:

German & English

Period:

Winter Semester

Content:

  • Low rank matrices
  • Separable expansions
  • Hierarchical matrix partitions
  • Hierarchical matrices
  • Formatted matrix operations
  • Applications
  • Additional topics (e.g. H2 matrices, matrix functions, tensor products)

Literature:

W. Hackbusch: Hierarchische Matrizen: Algorithmen und Analysis