The guide to PAMIR. Theory and use of parameterized adaptive multidimensional integration routines. (English) Zbl 1268.65034

Adler, Stephen L.

Hackensack, NJ: World Scientific (ISBN 978-981-4425-03-2/hbk; 978-981-4425-04-9/pbk). xi, 203 p. (2013).

The book under review is a technical presentation of a suite of FORTRAN programs for multidimensional numerical integration over hypercubes, simplices, and hyper-rectangles. This software is called PAMIR and can be downloaded from a website where one finds licensing fees and contact information. PAMIR stands for “Parameterized Adaptive Multi-dimensional Integration Routines” all of which is described through five chapters and one appendix divided into nine sections. Chapter 1 contains an introduction and further data related to copyright, credits, etc. Herein is where the author establishes the several goals that have to be reached in the following chapters.
Chapter 2 attempts to be a general purpose manual and it seems that it does. In particular, the notation used by PAMIR is stated and the base regions for the programs (the side 1 hypercube, the standard simplex, etc) are defined along with some of their applications. The rest of the chapter is devoted to explain how to use the main programs of PAMIR.
The examples in Chapter 3 allow comparison with other integration programs. Among the latter are CUBPACK, VEGAS and MISER.
Chapter 4 focuses on those aspects of PAMIR that make it different from other known programs. Thereby it attempts to specify what place this technology occupies within the current context.
Chapter 5 describes in some detail the construction of the algorithms that constitute PAMIR and the theory that lies behind each.
The appendix has a special practical importance. For example, the user can find in it several rules that can be used to test PAMIR routines.
The bibliography contains 45 items that are somehow related to the construction of PAMIR and were published between 1971 and 2008.

Reviewer: Jesus Illán González (Vigo)

MSC:

65D32	Numerical quadrature and cubature formulas
65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
41-04	Software, source code, etc. for problems pertaining to approximations and expansions
41A55	Approximate quadratures
41A63	Multidimensional problems
65Y15	Packaged methods for numerical algorithms

Keywords:

multidimensional integration; cubature formula; parameterized routine; automatic integration; adaptive integration scheme; hypercubes; simplices; hyper-rectangles; software; PAMIR

Software:

PAMIR; MISER3; VEGAS; CUBPACK