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What (who) is extremal spline - definition

Extremal graph

spline

WIKIMEDIA DISAMBIGUATION PAGE

Spline (device); Splines; Spline (disambiguation)

[spl??n]

¦ noun

1. a rectangular key fitting into grooves in the hub and shaft of a wheel, especially one formed integrally with the shaft which allows movement of the wheel on the shaft.

a corresponding groove in a hub along which the key may slide.

2. a slat.

3. a flexible wood or rubber strip used especially in drawing large curves.

4. Mathematics a continuous curve constructed so as to pass through a given set of points.

¦ verb secure by means of a spline.

?fit with a spline.

Origin

C18 (orig. East Anglian dialect): perh. related to splinter.

Cubic Hermite spline

$Cardinal spline example in 2D. The line represents the curve, and the squares represent the control points <math>\boldsymbol{p}_k</math>. Notice that the curve does not reach the first and last points; these points do, however, affect the shape of the curve. The tension parameter used is 0.1$

SPLINE WHERE EACH PIECE IS A THIRD-DEGREE POLYNOMIAL SPECIFIED IN HERMITE FORM: THAT IS, BY ITS VALUES AND FIRST DERIVATIVES AT THE END POINTS OF THE CORRESPONDING DOMAIN INTERVAL

Cubic spline; Cubic Hermite curve; Cubic Hermite curves; Cardinal spline; Catmull-Rom spline; Hermite curve; Hermite curves; Cubic interpolation; Cubic hermite spline; Catmull–Rom spline; Cspline; Catmull-Rom; Cubic Hermite Polynomial; Draft:Cubic interpolation

In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is, by its values and first derivatives at the end points of the corresponding domain interval.

https://en.wikipedia.org/wiki/Cubic_Hermite_spline

Spline

WIKIMEDIA DISAMBIGUATION PAGE

Spline (device); Splines; Spline (disambiguation)

·noun A long, flexble piece of wood sometimes used as a ruler.

II. Spline ·noun A rectangular piece fitting grooves like key seats in a hub and a shaft, so that while the one may slide endwise on the other, both must revolve together; a feather; also, sometimes, a groove to receive such a rectangular piece.

Wikipedia

Extremal graph theory

Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local substructure. Results in extremal graph theory deal with quantitative connections between various graph properties, both global (such as the number of vertices and edges) and local (such as the existence of specific subgraphs), and problems in extremal graph theory can often be formulated as optimization problems: how big or small a parameter of a graph can be, given some constraints that the graph has to satisfy? A graph that is an optimal solution to such an optimization problem is called an extremal graph, and extremal graphs are important objects of study in extremal graph theory.

Extremal graph theory is closely related to fields such as Ramsey theory, spectral graph theory, computational complexity theory, and additive combinatorics, and frequently employs the probabilistic method.

https://en.wikipedia.org/wiki/Extremal graph theory