A Survey of Preconditioned Iterative Methods (Pitman Research Notes in Mathematics Series)

Paperback, xii + 162 pages. Limited gentle wear, a faint number on the upper outer page edges. Interior is clean and bright with unmarked text, free of inscriptions and stamps, firmly bound. Straight spine. -- Solving large sparse linear systems from discretized partial differential equations requires efficient iterative methods; this book delivers a unified survey of preconditioned Krylov subspace techniques essential for researchers and practitioners in scientific computing. -- The text introduces iterative methods based on matrix splittings, covering classical techniques like Jacobi, Gauss-Seidel, and successive overrelaxation (SOR), as well as polynomial acceleration. It then develops the framework of Krylov subspace methods, deriving a generic algorithm that encompasses popular iterations such as the conjugate gradient (CG), GMRES, BICGSTAB, and QMR. Symmetric and nonsymmetric problems are addressed separately, with discussions on termination procedures and implementation efficiency. Preconditioning strategies form a central theme, including incomplete factorizations, approximate inverses, and polynomial preconditioners. The book also bridges algebraic tools with problem-oriented approaches like multigrid and domain decomposition, crucial for elliptic boundary value problems. -- This work offers a balanced blend of theoretical foundations, algorithmic details, and practical considerations, providing a durable framework for understanding solver performance. Its systematic treatment of preconditioning makes it an ideal resource for building robust simulation codes, calibrating models, and selecting optimal solution strategies for large-scale computations. It serves as both a concise learning guide and a conceptual reference for the mathematical underpinnings of modern iterative solvers.