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Everything about Numerical stability
Ability of numerical algorithms to remain accurate under small changes of inputs
In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context: one important context is numerical linear algebra, and another is algorithms for solving ordinary and partial differential equations by discrete approximation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Numerical stabilityA 5-minute orientation
- Skim a recent paper: Small-Signal Stability Analysis of Numerical Integration MethodsInfluential work since 2022
- Pick up a classic book: Comparison methods and stability theoryThe most-reprinted book on the subject
- Read the landmark paper: Numerical stability of GMRESCited 77 times
- Go sideways: Condition numberA closely related topic
- Go sideways: Fixed-point iterationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Numerical stability of GMRES
Numerical stability of nonorthogonal FDTD methods
Numerical experiments in climate stability
Iterative refinement implies numerical stability
Numerical experiments in boundary-layer stability
Computational Complexity and Numerical Stability
Slope Stability Analysis Using Numerical Modelling
Numerical stability in evaluating continued fractions
🆕 Influential since 2022
Small-Signal Stability Analysis of Numerical Integration Methods
Geophysical and numerical stability analysis of landslide incident
Assessing Slope Stability with an Improved 3D Numerical Manifold Method
On numerical stability of continued fractions
Numerical analysis of crack path stability in brittle porous materials
📚 Books worth reading
Comparison methods and stability theoryXinzhi Liu, David Siegel · 1994
Elementary stability and bifurcation theoryGérard Iooss, Gerard Iooss · 1980- 📕Nonlinear dispersive equationsJaime Angulo Pava · 2009
Strong stability preserving Runge-Kutta and multistep time discretizationsSigal Gottlieb · 2011
Bifurcations of planar vector fieldsFreddy Dumortier, F. Dumortier · 1991
The Concept of Stability in Numerical MathematicsWolfgang Hackbusch · 2014- 📕Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equationsChistopher A. Kennedy · 1999
- 📕Nonlinear dispersive equationsJaime Angulo Pava · 2009
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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