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.
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