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Everything about Smooth maximum
Mathematical approximation
In mathematics, a smooth maximum of an indexed family x1, ..., xn of numbers is a smooth approximation to the maximum function meaning a parametric family of functions such that for every , the function is smooth, and the family converges to the maximum function as . The concept of smooth minimum is similarly defined. In many cases, a single family approximates both: maximum as the parameter goes to positive infinity, minimum as the parameter goes to negative infinity; in symbols, as and as . The term can also be used loosely for a specific smooth function that behaves similarly to a maximum, without necessarily being part of a parametrized family. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Smooth maximumA 5-minute orientation
- Skim a recent paper: Spreading of a droplet impacting on a smooth flat surface: How liquid viscosity influences the maximum spreading time and spreading ratioInfluential work since 2022
- Pick up a classic book: Nonlinear elliptic partial differential equationsThe most-reprinted book on the subject
- Read the landmark paper: Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable modelsCited 262 times
- Go sideways: Liouville functionA closely related topic
- Go sideways: Exponential mechanismA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models
Partial Shading Detection and Smooth Maximum Power Point Tracking of PV Arrays Under PSC
Analytical Consideration for the Maximum Spreading Factor of Liquid Droplet Impact on a Smooth Solid Surface
Smooth nonparametric maximum likelihood estimation for population pharmacokinetics, with application to quinidine
Smooth, second order, non‐negative meshfree approximants selected by maximum entropy
Smooth Convex Approximation to the Maximum Eigenvalue Function
Maximum likelihood estimation of smooth monotone and unimodal densities
Maximum Likelihood Estimation for a Smooth Gaussian Random Field Model
🆕 Influential since 2022
Spreading of a droplet impacting on a smooth flat surface: How liquid viscosity influences the maximum spreading time and spreading ratio
Smooth path planning under maximum curvature constraints for autonomous underwater vehicles based on rapidly-exploring random tree star with B-spline curves
Universal Model for Predicting Maximum Spreading of Drop Impact on a Smooth Surface Developed Using Boosting Machine Learning Models
Maximum Spreading of Hydrofluoroether Drop Impacting on a Smooth Surface
Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model
📚 Books worth reading
- 📕Nonlinear elliptic partial differential equationsWorkshop in Nonlinear Elliptic Partial Differential Equations (2009 Université libre de Bruxelles) · 2011
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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