Systems of linear equations are ubiquitous in numerical analysis
and scientific computing. and iterative methods are indispensable
for the numerical treatment of such systems. This book offers a
rigorous introduction to fundamental iterative methods for systems
of linear algebraic equations. The book distinguishes itself from
other texts on the topic by providing a straightforward yet
comprehensive analysis of the Krylov subspace methods, approaching
the development and analysis of algorithms from various
perspectives, and going beyond the standard description of
iterative methods by connecting them in a natural way to the idea
of preconditioning. The book supplements standard texts on
numerical mathematics for first-year graduate and advanced
undergraduate courses and is suitable for advanced graduate classes
covering numerical linear algebra and Krylov subspace and multigrid
iterative methods. It will be useful to researchers interested in
numerical linear algebra and engineers who use iterative methods
for solving large algebraic systems.
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