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Polyharmonic spline

In applied mathematics, polyharmonic splines are used for function approximation and data interpolation. They are very useful for interpolating and fitting scattered data in many dimensions. Special cases include thin plate splines and natural cubic splines in one dimension.

Reason for the name "polyharmonic", Definition & Polyharmonic smoothing splines

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Reason for the name "polyharmonic"

Partial differential equationLaplace operatorBiharmonic equationDirac delta functionComputer algebra system
5 related topics

Definition

Radial basis functionsNatural logarithmNull space
3 related topics

Polyharmonic smoothing splines

Thin plate energy functionalMulti-indexEuler–Lagrange equation
3 related topics

Fast construction and evaluation methods

ALGLIBDomain decomposition methods
2 related topics

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Overview

Definition

Discussion

Fast construction and evaluation methods

Reason for the name "polyharmonic"

Polyharmonic smoothing splines

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Map overview Semantic statistics

Polyharmonic spline

Nodes25
Edges24
Triples28
Avg. degree1.92
Density0.08
Components1

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Polyharmonic spline

Top relations

has method · 9
Polyharmonic spline → As, First, MN, One, RBFInterpolator, Recently, Such, The, This
related to Discussion · 6
Polyharmonic spline → For, Gaussian, If, Main, The, This
related to Examples · 5
Polyharmonic spline → Finally, Note, Since, The, This
related to External links · 3
Polyharmonic spline → An, Computer Code Polyharmonic Spline, Matlab/Octave
related to Polyharmonic smoothing splines · 3
Polyharmonic spline → For, In, Polyharmonic
is a · 1
Polyharmonic spline → linear combination of polyharmonic radial basis functions
related to Definition · 1
Polyharmonic spline → RBFs

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Important terminology

displaystyle polyharmonic mathbf spline equation function splines system delta textstyle interpolation linear basis term solution radial functions example first textrm

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Polyharmonic splineis alinear combination of polyharmonic radial basis functions0.90text
Polyharmonic splinehas methodOne0.60section
Polyharmonic splinehas methodAs0.60section
Polyharmonic splinehas methodMN0.60section
Polyharmonic splinehas methodThis0.60section
Polyharmonic splinehas methodSuch0.60section
Polyharmonic splinehas methodRBFInterpolator0.60section
Polyharmonic splinehas methodThe0.60section
Polyharmonic splinehas methodRecently0.60section
Polyharmonic splinehas methodFirst0.60section
Polyharmonic splinerelated to DefinitionRBFs0.60section
Polyharmonic splinerelated to DiscussionThe0.60section

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