1.7 Introduction to the Remainder of the Book

In Chapter 2, we will discuss solution of systems of linear equations. These methods allow us to use computers to solve systems of equations far larger than those we could solve by hand. An efficient linear system solver is a basic building block for more complicated programs involved in computer simulations.

Chapter 3 introduces methods for data fitting. Given a set of data, we will determine a function whose graph passes through or near the data points. Two basic methods will be introduced: interpolation, which is used only when the data set is believed to contain exact values, and least squares data fitting, which is suitable when the data values may contain measurement or other errors.

In Chapter 4, we consider the solution of nonlinear equations. We will introduce several methods designed to find a zero of a nonlinear equation. These methods will also introduce the concept of iteration.

In Chapter 5, we return to the methods described in Chapter 2 and compute the amount of work that will be required to calculate a solution for an n x n linear system. These cost values are used to compare methods and to identify efficient techniques.

Chapter 6 returns to the topic of iteration, introduced in Chapter 4. After a discussion of ways in which iteration techniques are derived, we consider some iterative techniques for solving linear systems.

Throughout this book, we assume that the reader is familiar with matrix operations. A review of matrix properties and operations is included at the end of the book.