Computer arithmetic and validity. Theory, implementation, and applications (Q5917924)

The second edition of this book retains the structure and the content of the first edition [(2008; Zbl 1149.65034)]: theory implementation and applications of computer arithmetic. The advanced computer arithmetic is performed in finite precision over most spaces of numerical computing: scalars, vectors and matrices with elements that are reals, complex numbers, real intervals or complex intervals. The result of any computer operation should differ from the correct result by at most one rounding. The goal is to improve the accuracy of the numerical computations and to control the quality of the computed results. The present second edition is corrected and enhanced. Large portions of several chapters are newly rewritten, some in the spirit of the discussions in the IEEE working group P1788 for standard of interval arithmetic. The list of references contains 60 new titles, however, not all items are cited in the text. The book can be used as an ``undergraduate textbook in mathematics and computer science as well as a reference work for research in computer arithmetic, scientific computing and applied mathematics''.