Claude Brezinski is emeritus professor of numerical analysis at the University of Sciences and Technologies of Lille (Laboratory Paul Painlevé, UMR CNRS 8524), France. His work mainly concerns extrapolation methods, orthogonal polynomials, Padé and rational approximation and numerical linear algebra. He also published several papers and books on the history of sciences.

Dominique Tournès is professor of mathematics and history of mathematics at the University of La Réunion (Laboratory of Mathematics and Computer Science, EA 2525), France and associate researcher at the SPHERE laboratory (UMR 7219, CNRS and University Paris-Diderot, France). His work focuses on the history of calculation methods and instruments since the seventeenth century, particularly regarding differential equations.

The only existing book on the life and the works of Cholesky and contemporaries

Reproduction of an unpublished manuscript on graphical calculation

English translation of his unpublished paper on the solution of systems of linear equations and further unpublished documents with historical and mathematical commentaries

Preface.- Biography of Cholesky.- Cholesky's family.- On topography.- The method of Cholesky for linear systems.- Other works of Cholesky.- Léon Eyrolles and his superior school.- An unpublished book by Cholesky.- Ernest Benoît.- Documents.- Acknowledgments.- Bibliography.- Index.