Multigrid and Iterative Solvers
Krylov subspace methods, preconditioning, and multigrid hierarchies.
Multigrid and Iterative Solvers. Krylov subspace methods, preconditioning, and multigrid hierarchies.
Foundations and canonical references
The standard treatments of multigrid and iterative solvers approach the subject from complementary angles. Trottenberg, Multigrid (2001) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Saad, Iterative Methods for Sparse Linear Systems (2003) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for multigrid and iterative solvers include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2001Multigridtrottenberg-2001, oosterlee-2001, schuller-2001
- textbook · primary · 2003Iterative Methods for Sparse Linear Systemssaad-2003
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