Support point

Support point is a term from numerical mathematics . It denotes the arguments of functions that are used for the further calculation. The term is used, for example, in interpolation or numerical integration . The associated functional value at the interpolation point is sometimes called the interpolation value , the ordered pair of interpolation point and interpolation value is then called the interpolation point .

example

Support points of ${\displaystyle x_{0}=0,x_{1}=1,x_{2}=2}$ ${\displaystyle f(x)=x^{2}}$

One would like to interpolate the function using three given points: A (0/0), B (1/1), C (2/4). Consequently, we have three support points, namely , , . The associated support values ​​are ${\displaystyle f(x)=x^{2}}$ ${\displaystyle x_{0}=0}$ ${\displaystyle x_{1}=1}$ ${\displaystyle x_{2}=2}$

${\displaystyle f(0)=0}$

${\displaystyle f(1)=1}$

${\displaystyle f(2)=4}$

or the support points are , and . ${\displaystyle (0,0)}$ ${\displaystyle (1,1)}$ ${\displaystyle (2,4)}$

literature

• Hans Rudolf Schwarz, Norbert Köckler: Numerical Mathematics , BG Teubner Stuttgart 2003