Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony's problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.
Tomas Sauer holds the chair of Mathematics for Image Processing at the University of Passau. His research interests include signal and image processing, computer algebra and numerical methods for the solution of real world applied problems. He founded the Fraunhofer IIS research group "Knowledge based image processing" at the University of Passau that deals with the development of methods for handlig large scale industrial tomography data.
1. Continued fractions and what can be done with them.- 2. Continued fractions of real numbers.- 3. Rational functions as continued fractions of polynomials.- 4.Continued Fractions and Gauss.- 5. Continued Fractions and Prony.- 6. Digital Signal processing.- 7.Contined Fractions, Hurwitz and Stieltjes.