Advances in Numerical Analysis Emphasizing Interval Data

6 Interpolation from the Linear Algebra Point of View

DOI: 10.1201/9781003218173-6

6.1 Introduction

In this section, we study interpolation from another perspective. As we have already seen, each of the interpolation functions is examined in its own vector space, each of which has at least one basis. If we consider the nature of the interpolation problem, we can say that an interpolation function is obtained by quantifying and forming a system of linear equations. Quantifying means calculating the value of the function at different points $x_i$ and obtaining different values of $f_i\in ℝ$, so this quantifying operation can be considered as a linear functional such as $L$ so that for the interpolation function $p$,

$$L_i\left(p\right)=p\left(x_i\right)=f_i,i=0,1,\dots ,m$$ (6.1)

So according ...