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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.