I applaud the authors' decision to hold off on this for as long as possible, but to include it. The coverage here is effective, including examples of Newton's method, vectors and matrices, passing arrays to functions, and another implementation of Gaussian elimination. Even here, however, the code doesn't really look like the typical numerical analysis textbook pseudocode. Rather than a monolithic structure of sequences of nested loops, a main function and several auxiliary functions are used, so that there is still the flavor of top-down analysis. Chapter 9 covers numerics , including number types, random numbers, Precision and Accuracy , and examples of numerical difficulties.
Gaussian elimination is revisited yet again.
Partial pivoting is presented to ameliorate bad conditioning, and is shown to be somewhat successful for linear systems problems with Hilbert matrices. An exercise discusses scaled partial pivoting. As with the previous chapter, I find this material to be well placed. Too many numerical methods books start with floating point representation and catastrophic cancellation in chapter one, when the students need to learn what will work, not what won't. Only later, after they've seen things go wrong in the output but can't find errors in their programs, are students ready to hear about bad conditioning.