Introduction

Since most algorithms and templates presented in detail in this book are iterative projection methods designed for solving large sparse eigenvalue problems, in this chapter, we begin with a discussion of the general framework of these iterative projection methods. It is well known that most of these methods provide rapid approximations to well-separated extremal eigenvalues. However, quite often, the sought-after eigenvalues may not be separated and are interior. The spectral transformation to be outlined in §3.3 is a practical tool for transforming the sought-after eigenvalues to well-separated extremal eigenvalues.