Many properties of the IEEE-754 floating-point number system are taken for granted in
modern computers and are deeply embedded in compilers and low-level software routines …

This tutorial gives a brief introduction to computable analysis. The objective of this theory is
to study algorithmic aspects of real numbers, real number functions, subsets of real …

In the nearly seven years since I finished writing the first edition of this book research on the
accuracy and stability of numerical algorithms has continued to flourish and mature. Our …

Functions of matrices have been studied for as long as matrix algebra itself. Indeed, in his
seminal A Memoir on the Theory of Matrices (1858), Cayley investigated the square root of a …

Before using interval analysis as a basic tool in the following chapters, we shall now
introduce its main concepts. Section 2.2 recalls fundamental notions on set operators, set …

Constraint programming is a powerful paradigm for solving combinatorial search problems
that draws on a wide range of techniques from artificial intelligence, computer science …

This book presents a broad overview of numerical methods for students and professionals in
computationally oriented disciplines who need to solve mathematical problems. It differs …

This article presents a multiple-precision binary floating-point library, written in the ISO C
language, and based on the GNU MP library. Its particularity is to extend to arbitrary …

This text explains the fundamental principles of algorithms available for performing
arithmetic operations on digital computers. These include basic arithmetic operations like …

Residue number systems (RNSs) and arithmetic are useful for several reasons. First, a great
deal of computing now takes place in embedded processors, such as those found in mobile …