This self-contained introduction to numerical linear algebra provides a
comprehensive, yet concise, overview of the subject. It includes
standard material such as direct methods for solving linear systems and
least-squares problems, error, stability and conditioning, basic
iterative methods and the calculation of eigenvalues. Later chapters
cover more advanced material, such as Krylov subspace methods, multigrid
methods, domain decomposition methods, multipole expansions,
hierarchical matrices and compressed sensing. The book provides rigorous
mathematical proofs throughout, and gives algorithms in general-purpose
language-independent form. Requiring only a solid knowledge in linear
algebra and basic analysis, this book will be useful for applied
mathematicians, engineers, computer scientists, and all those interested
in efficiently solving linear problems.