Numerical Linear Algebra for Signal Processing

What it is about

You will learn numerical methods of linear algebra used in digital signal processing systems with finite precision. In the end you can safely apply algorithms such as QR, Cholesky and SVD decompositions as well as methods for solving systems of equations and and least squares problems, analyze their complexity, conditioning and stability, and evaluate them for practical signal processing tasks.

What you will be able to do

• Apply numerical algorithms of linear algebra for practical signal processing
• Analyze the computational complexity of algorithms
• Assess the conditioning of a problem (norm-wise and component-wise)
• Evaluate the stability of algorithms using forward- and backward-error analysis
• Analyze Householder-QR, back substitution, Gauss elimination and Cholesky
• Derive defined matrix structures with Householder reflections and Givens rotations
• Implement fundamental steps of eigenvalue and singular value decompositions

What the module consists of

• VorlesungVermittlung der theoretischen Grundlagen und Algorithmen
• Übungen / TutorienVertiefung und Anwendung durch Aufgaben; wiederholendes Festigen
• Freiwillige ProjekteOptionales Vertiefen durch Analyse und eigene Lösungen (max. 25% der Note)

Teaching method

• Lehrvortrag (teacher-centered)Einführung und Strukturierung der Themen während der Vorlesung
• Übungen student-centeredPraktisches Einüben, Festigen und Anwenden des Stoffes
• Freiwillige ProjektarbeitEigenständiges Vertiefen und kreative Problemlösungen; bis 25% der Endnote