Claude Brezinski Livres

The book delves into the extensive history of continued fractions, tracing their origins back to Euclid's algorithm. It highlights their long-standing use prior to formal recognition and emphasizes their significance in various mathematical developments, including the proof of the transcendence of e in 1882. Continued fractions and Pade approximants are shown to be pivotal in modern spectral theory and have applications across pure and applied mathematics, numerical analysis, number theory, computer science, and more.

Focusing on the principles of control theory, this book explores how systems transform inputs into outputs through feedback mechanisms governed by differential equations. It delves into the interdisciplinary nature of control theory, intersecting with differential equations, system theory, and statistics. The text highlights the computational challenges involved, covering topics such as numerical analysis, linear algebra, root localization, and optimization. While it presents various numerical analysis issues, it emphasizes that it is not solely about control theory itself.

This book traces the life of Cholesky (1875-1918), and gives his family history. After an introduction to topography, an English translation of an unpublished paper by him where he explained his method for linear systems is given, studied and replaced in its historical context. His other works, including two books, are also described as well as his involvement in teaching at a superior school by correspondence. The story of this school and its founder, Léon Eyrolles, are addressed. Then, an important unpublished book of Cholesky on graphical calculation is analyzed in detail and compared to similar contemporary publications. The biography of Ernest Benoit, who wrote the first paper where Cholesky ́s method is explained, is provided. Various documents, highlighting the life and the personality of Cholesky, end the book.