Steklov function
E910283
The Steklov function is a mathematical construct used in approximation theory and numerical analysis, often involving integral averaging to smooth or approximate other functions.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
approximation tool
ⓘ
mathematical concept ⓘ smoothing operator ⓘ |
| appliedTo |
discrete data via suitable discretization
ⓘ
functions defined on real intervals ⓘ |
| comparedTo |
Cesàro-type averaging methods
ⓘ
other smoothing kernels such as Fejér means ⓘ |
| context |
approximation of continuous functions
ⓘ
stability analysis of numerical schemes ⓘ theory of positive linear operators ⓘ |
| dependsOn |
choice of averaging kernel or window
ⓘ
size of averaging interval or parameter ⓘ |
| effect |
damps high-frequency components of a function
ⓘ
retains low-frequency or large-scale behavior ⓘ |
| field |
approximation theory
ⓘ
numerical analysis ⓘ |
| hasAlternativeName |
Steklov averaging function
NERFINISHED
ⓘ
Steklov mean ⓘ |
| hasNotation | often denoted by S_h f or similar symbols ⓘ |
| historicalContext | developed in the context of early 20th century Russian analysis ⓘ |
| input | real-valued function ⓘ |
| namedAfter | Vladimir Andreevich Steklov NERFINISHED ⓘ |
| namedEntityType | mathematical object ⓘ |
| output | smoothed real-valued function ⓘ |
| property |
bounded operator on many function spaces
ⓘ
can improve smoothness of functions ⓘ can preserve continuity under suitable conditions ⓘ linear operator (in common formulations) ⓘ |
| purpose |
approximating functions
ⓘ
reducing oscillations of a function ⓘ regularizing irregular data ⓘ smoothing functions ⓘ |
| relatedTo |
convolution operators
ⓘ
integral transforms ⓘ moving average operators ⓘ regularization methods ⓘ |
| typicalOperation |
integral averaging
ⓘ
local averaging over an interval ⓘ |
| usedFor |
constructing approximations with controlled smoothness
ⓘ
filtering noise from numerical data ⓘ preprocessing functions before numerical differentiation ⓘ |
| usedIn |
construction of approximating sequences
ⓘ
error analysis of approximation methods ⓘ numerical solution of differential equations ⓘ signal smoothing in numerical data ⓘ study of convergence of approximations ⓘ |
Referenced by (1)
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