Deterministische und stochastische Rundungsfehleranalysen von schnellen trigonometrischen Algorithmen in Gleitkomma- bzw. Festkomma-Arithmetik

In dieser Dissertation wird eine umfassende und einheitliche Stabilitätsanalyse sowohl in Festkomma- als auch in Gleitkomma-Arithmetik für eine Klasse von schnellen DCT- und DST-Algorithmen durchgeführt, welche auf Faktorisierungen der orthogonalen Transformationsmatrizen in Produkte von dünnbesetzten orthogonalen Matrizen beruhen. Neben Untersuchungen für den ungünstigsten Fall (worst case) wird auch jeweils eine stochastische Rundungsfehleranalyse (average case) durchgeführt, welche ohne die in der Bildverarbeitung selten gegebene Unkorreliertheit der Eingangsdaten auskommt.In this thesis, a comprehensive and unified stability analysis for a class of fast DCT (discrete cosine transform) and DST (discrete sine transform) algorithms is performed, both for fixed-point and floating-point arithmetic. Each of them is based on a factorization of the underlying orthogonal transform matrix into a product of sparse orthogonal matrices. Additionally to worst case analysis, also the average case is considered using stochastic models for the relative and absolute roundoff errors. Particularly with regard to applications in digital image processing, the stochastic analysis of roundoff error is done without assuming the data to be uncorrelated or independent

Designing Digital Self-Assessment and Feedback Tools as Mentoring Interventions in Higher Education

Higher education in Germany traditionally follows a one-size-fits-all paradigm. The ignorance of diverse students’ needs jeopardizes high-quality and equal educational opportunities for all. Digital technologies can provide economical solutions to individualize teaching and learning, even in large university classes. However, their design has to incorporate pedagogical theories, specific contextual requirements, and users’ needs (Laurillard, 2008). In this project contribution, we want to demonstrate our approach to this challenge. We briefly describe how we connected the pedagogical concept of mentoring to theories of self-regulated learning and used this as a framework for developing formative assessment and automated feedback tools as digital mentoring interventions. The mentoring nterventions aim at facilitating self-regulated learning, especially self-monitoring and strategy-adaption. We present three different implementations in structured and illstructured domains and the key results of a qualitative evaluation survey. [Aus: Introduction

Designing Digital Self-Assessment and Feedback Tools as Mentoring Interventions in Higher Education

Higher education in Germany traditionally follows a one-size-fits-all paradigm. The ignorance of diverse students’ needs jeopardizes high-quality and equal educational opportunities for all. Digital technologies can provide economical solutions to individualize teaching and learning, even in large university classes. However, their design has to incorporate pedagogical theories, specific contextual requirements, and users’ needs (Laurillard, 2008). In this project contribution, we want to demonstrate our approach to this challenge. We briefly describe how we connected the pedagogical concept of mentoring to theories of self-regulated learning and used this as a framework for developing formative assessment and automated feedback tools as digital mentoring interventions. The mentoring nterventions aim at facilitating self-regulated learning, especially self-monitoring and strategy-adaption. We present three different implementations in structured and illstructured domains and the key results of a qualitative evaluation survey. [Aus: Introduction

Designing Digital Self-Assessment and Feedback Tools as Mentoring Interventions in Higher Education

Higher education in Germany traditionally follows a one-size-fits-all paradigm. The ignorance of diverse students’ needs jeopardizes high-quality and equal educational opportunities for all. Digital technologies can provide economical solutions to individualize teaching and learning, even in large university classes. However, their design has to incorporate pedagogical theories, specific contextual requirements, and users’ needs (Laurillard, 2008). In this project contribution, we want to demonstrate our approach to this challenge. We briefly describe how we connected the pedagogical concept of mentoring to theories of self-regulated learning and used this as a framework for developing formative assessment and automated feedback tools as digital mentoring interventions. The mentoring nterventions aim at facilitating self-regulated learning, especially self-monitoring and strategy-adaption. We present three different implementations in structured and illstructured domains and the key results of a qualitative evaluation survey. [Aus: Introduction