0
votes
2answers
35 views

Find limits of value/derivatives defining a polynomial at 2 points to bound it in between

The following properties define the polynomial $p(x)$ uniquely: $\text{deg}(p(x))=7\\p(-1)=y_1,\ p'(-1)=d_{1,1},\ p''(-1)=d_{2,1},\ p'''(-1)=d_{3,1}\\ p(1)=y_2,\ \ \ \ p'(1)=d_{1,2},\ \ \ \ ...
4
votes
1answer
217 views

Does the total variation of a function bound its numerical integration error, much like its first derivative?

When estimating the convergence of a Riemann sum to its integral, or equivalently the error in numerical integration, the commonly used bound is by upper bounding it's first derivative (see, for ...