The book offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by
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.
keywords: systems of linear algebraic equations, iterative methods, Krylov subspaces, preconditioners, convergence analysis
Maxim A. Olshanskii is a professor in the Department of Mathematics at the University of Houston and an adjunct professor at Emory University and Moscow Institute of Physics and Technology. He is the Managing Editor of the Journal of Numerical Mathematics and 2001 recipient of the Young Scientists Award of the European Academy of Sciences. Eugene E. Tyrtyshnikov is Director of the Institute of Numerical Mathematics of the Russian Academy of Sciences and Professor and Chairman at the Faculty of Computational Mathematics and Cybernetics of Moscow State University. He became a Corresponding Member of the Russian Academy of Sciences in 2006. He serves as associate editor of Linear Algebra and Its Applications and as a member of editorial boards of seven other journals.
List of Figures; List of Algorithms; Preface; 1 Krylov Subspace Methods; 2 Toeplitz Matrices and Preconditioners; 3 Multigrid Preconditioners; 4 Preconditioners by Space Decomposition; 5 Some Applications; Bibliography; Index