SIAM

A first course in numerical methods.

Ascher and Greif (both U. of British Columbia) present a textbook they developed from courses they have taught for over 25 years to computer scientist students. The idea is to present enough basic principles about scientific computing that students can notice if one the standard software packages has produced a result that could not possibley be correct, then to figure out why. The theory they present is not deep and abstract, they say, but just a layer two underpinning methods, though mathematical justifications are provided. Most of the material can be covered in two semesters, with additional material to provide flexibility or extra assignments for hot shots. (Annotation ©2011 Book News Inc. Portland, OR)

Graph algorithms in the language of linear algebra.

Mathematicians and computer scientists address some of the challenges that remain from the fruitful combination of graph algorithms and parallel computing. They exploit the duality between the canonical representation of graphs as abstract collections of vertices with edges and a sparse adjacency matrix representation. In so doing, they show how to leverage existing parallel matrix computation techniques, as well as the large amount of software infrastructure that exists for these computations, to implement efficient and scalable parallel graph algorithms. In sections on algorithms, data, and computation, they considers such topics as graphs and matrices, the Kronecker theory of power law graphs, and the parallel mapping of sparse computations. (Annotation ©2011 Book News Inc. Portland, OR)

Semismooth Newton methods for variational inequalities and constrained optimization problems in function spaces.

Ulbrich (Technical U. Munich) describes a successful class of methods for solving optimization problems with partial differential equations and inequality constraints as well as variational inequalities in function spaces. The approach combines the idea of non-smooth point-wise reformulations of system inequalities with the concept of semi-smooth Newton methods. His topics include elements of finite-dimensional non-smooth analysis, smoothing steps and regularity conditions, mesh independence, state-constrained and related problems, and the optimal control of compressible and incompressible Navier-Stokes flow. (Annotation ©2011 Book News Inc. Portland, OR)