Choice Review

Gill and colleagues stress the need for a work that unifies treatment of three distinct areas: fundamentals of numerical analysis and scientific computing; solutions to linear systems and linear least-squares problems, and the updating of matrix factorizations; and numerical optimization methods for both linear and nonlinear programming. There is not, in fact, a sharp line between the first two topics. Although some numerical analysis texts go more heavily into integral or differential equations, almost all contain some material on the classic problems of linear analysis, and some (e.g., K.E. Atkinson's Introduction to Numerical Analysis, 2nd ed., 1989; 1st ed., CH, May'79) make linear analysis a principal object to study. There are, conversely, books on numerical linear algebra, (e.g., G.W. Stewart, Introduction to Matrix Computations, CH, Jan'74) that have a good deal to say about numerical analysis. The main thrust of Gill and colleagues is right, however. By focusing numerical analysis on linear systems, and then building on this foundation, they are able to treat linear programming with much more attention to computational problems than is to be found in any text of which this reviewer is aware. Full utilization of software tools such as Mathlab and Mathematica also enhances the authors' ability to make their points very forcibly. -W. Roberts, Macalester College