Numerical integration in arbitrary-precision ball arithmetic

Intégration numérique avec erreur bornée en précision arbitraire. (Arbitrary precision numerical integration with bounded error)

On Lambert's W Function

Lambert's W function is the inverse of the function w 7 ! we w. It has been applied in combinatorics, number theory, uid mechanics, quantum mechanics, and biochemistry. Some of these applications are brieey described here. This paper presents a new discussion of the complex branches of W, asymptotic expansions valid for all branches, an eecient numerical procedure for evaluating the function to...

Extrapolation Methods in Mathematica 1

This article outlines design and implementation details of the framework for one step methods for solving ordinary differential equations in Mathematica. The solver breaks up the solution into three main phases for equation processing and classification, numerical solution and processing of results. One of the distinguishing features of the framework is the hierarchical nature of the method inv...

Stochastic Arithmetic in Multiprecision

Floating-point arithmetic precision is limited in length the IEEE single (respectively double) precision format is 32-bit (respectively 64-bit) long. Extended precision formats can be up to 128-bit long. However some problems require a longer floating-point format, because of round-off errors. Such problems are usually solved in arbitrary precision, but round-off errors still occur and must be ...

On the LambertW function

The Lambert W function is defined to be the multivalued inverse of the function w 7→ we. It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches of W , an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for...