Everything about Smoothness
Degree of differentiability of a function or map
In calculus and mathematical analysis, the smoothness of a function describes the number of times it can be differentiated without producing discontinuities. The smoothness, or differentiability class, is an integer such that a function has all derivatives up to order, and such that all of these derivatives are continuous. One says that such a function has class. For example, the absolute value function has class, because it is continuous, but not differentiable. Generally, the term smooth function refers to a -function, that is a function having derivatives of all orders. However, it may also mean "sufficiently differentiable" for the problem under consideration. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: SmoothnessA 5-minute orientation
- Skim a recent paper: Guaranteed Tensor Recovery Fused Low-rankness and SmoothnessInfluential work since 2022
- Pick up a classic book: Muscarinic receptor subtypes in smooth muscleThe most-reprinted book on the subject
- Read the landmark paper: Adapting to Unknown Smoothness via Wavelet ShrinkageCited 3,429 times
- Go sideways: Differentiable vector-valued functions from Euclidean spaceA closely related topic
- Go sideways: Sobolev spaceA closely related topic
📖 Definitions
Noun The condition of being smooth; the degree or measure of said condition.
Noun The highest order of derivative (the differentiability class) over a given domain.
Noun The quantity measured by the modulus of smoothness.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Adapting to Unknown Smoothness via Wavelet Shrinkage
Sparsity and Smoothness Via the Fused Lasso
Persistence and Smoothness of Invariant Manifolds for Flows
A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors
Movement Smoothness Changes during Stroke Recovery
An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences
Harnessing Smoothness to Accelerate Distributed Optimization
Fast Stable Direct Fitting and Smoothness Selection for Generalized Additive Models
🆕 Influential since 2022
Guaranteed Tensor Recovery Fused Low-rankness and Smoothness
Hyperspectral Anomaly Detection With Tensor Average Rank and Piecewise Smoothness Constraints
Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices
Reconstruction of Time-Varying Graph Signals via Sobolev Smoothness
Influence of Three-Dimensional Printing Parameters on Compressive Properties and Surface Smoothness of Polylactic Acid Specimens
📚 Books worth reading
Muscarinic receptor subtypes in smooth muscleRichard M. Eglen · 1997- 📕EDHF 2000Paul M. Vanhoutte · 2001
The Vascular Smooth Muscle CellStephen M. Schwartz · 1995
Control theoretic splinesMagnus Egerstedt · 2009
Airways Smooth MuscleD. Raeburn · 1994
Smoothing splinesYuedong Wang · 2011
A functional view of smooth muscleG. Christ · 2000- 📕Regulation of the contractile cycle in smooth muscleDavid J. Hartshorne · 1995
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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