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Everything about Preconditioner
Transforms equations for numerical solution
In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing a condition number of the problem. The preconditioned problem is then usually solved by an iterative method. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: PreconditionerA 5-minute orientation
- Skim a recent paper: A GPU-based multilevel additive schwarz preconditioner for cloth and deformable body simulationInfluential work since 2022
- Pick up a classic book: Introduction to linear algebraThe most-reprinted book on the subject
- Read the landmark paper: BoomerAMG: A parallel algebraic multigrid solver and preconditionerCited 723 times
- Go sideways: Modified Richardson iterationA closely related topic
- Go sideways: Conjugate gradient squared methodA closely related topic
📖 Definitions
Noun A matrix that has a smaller condition number than another.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
BoomerAMG: A parallel algebraic multigrid solver and preconditioner
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
An Optimal Circulant Preconditioner for Toeplitz Systems
A Multiplicative Calderon Preconditioner for the Electric Field Integral Equation
A Preconditioner for Generalized Saddle Point Problems
A Preconditioner for Substructuring Based on Constrained Energy Minimization
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
🆕 Influential since 2022
A GPU-based multilevel additive schwarz preconditioner for cloth and deformable body simulation
On τ-preconditioner for a novel fourth-order difference scheme of two-dimensional Riesz space-fractional diffusion equations
A reverse augmented constraint preconditioner for Lagrange multiplier methods in contact mechanics
Preconditioner influence on twin-screw extrusion cooking of starch-based feed pellets: The example of Fish Feed
Deep optics preconditioner for modulation-free pyramid wavefront sensing
📚 Books worth reading
Introduction to linear algebraGilbert Strang · 1998
Numerical Mathematics and Advanced Applications 2011Andrea Cangiani · 2013
Schwarz Methods and Multilevel Preconditioners for Boundary Element MethodsErnst Peter Stephan, Thanh Tran · 2021
Diagonal scalings of the Laplacian as preconditioners for other elliptic differential operatorsAnne Greenbaum · 1990- 📕Graph embedding techniques for bounding condition numbers of incomplete factor preconditionersStephen Guattery · 1997
An optimal domain decomposition preconditioner for the finite element solution of linear elasticity problemsBarry F. Smith · 1989
Resource Recovery, Confinement, and Remediation of Environmental HazardsJohn Chadam · 2002
Iterative Methods and Preconditioners for Systems of Linear EquationsGabriele Ciaramella, Martin J. Gander · 2022
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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