Displacement structure of matrices: fundamentals and applications




It is the presence of special structure, and its exploitation, that occupy engineers and applied mathematicians in fields where standard general algorithms are well known, for example, Gaussian elimination for general systems of linear equations. Examples of structure are systems with Toeplitz (or Hankel or Cauchy or Vandermonde or…) coefficient matrices, for which there exist fast solution algorithms with many nice hardware and software features. However often the structure is implicit, e.g., as in matrices that are combinations of products of structured matrices and their inverses, and the existence of fast algorithms for such systems is not obvious. The concept of Displacement Structure is a uniform and powerful way of capturing and exploiting both explicit and implicit structure. For example, structured matrices and their inverses and products thereof all have low “displacement rank”, a fact that enables the development of fast algorithms in many fields including communications and signal processing. 


In this talk, we shall present an introduction to the fundamental concepts of the theory and note some recent developments and applications.


Brief bio Prof. Kailath


Video de la sesión

Galería fotográfica



Wednesday, June 25, 2014 - 4:00pm