Tagged Questions
1
vote
1answer
159 views
Interpolation inequality
Lef $u$ be at least a $C^2$ function on $\mathbb{R}^n$. Let's denote the gradient by $D$. Also, (using the multiindex notation), define the seminorm $$||D^ku|| = ...
0
votes
1answer
38 views
Unique solution on subspaces whose union is dense implies unique solution globally?
Let $V$ denote the space of all $f : [0,1] \to {\mathbb R}$ such that the second derivative $f''$ is continuous except on a finite set, equipped with the norm
$N(f)=|f(0)|+|f’(0)|+||f''||_{\infty}$ ...
2
votes
1answer
128 views
Why is this a linear interpolation?
Let $J_{k,n}$ be the dyadic partition of $[0,1]$, i.e. $n\in \mathbb{N}_0,k=1,\dots,2^n$, $J_{k,n}:=((k-1)2^{-n},k2^{-n}]$ and we denote with $\phi_{n,k}$ the Schauder functions over $J_{k,n}$, i.e. ...
2
votes
0answers
76 views
explicit error bounds for Multivariate interpolation
I want to interpolate a function of $d$ variables over a Cartesian grid, using multivariate interpolation, while characterizing interpolation error in terms of bounds on partial derivatives of the ...
1
vote
1answer
230 views
A problem on Lagrange interpolation polynomials
Based on a previous question, I had the following conjecture and was wondering if anyone knew how to prove it or find a counterexample.
Consider the polynomial $$ ...
2
votes
1answer
114 views
Short argument/reference for uniform continuity of piecewise linear interpolation
I have a piecewise linear interpolation:
$$ B(t) = \frac{t_{l+1}-t}{t_{l+1}-{t_{l}}} B_l + \frac{t-t_l}{t_{l+1}-{t_{l}}} B_{l+1}
\quad \text{ if $t \in (t_l, t_{l+1})$;}$$
$B(t_l)=B_{l}$ and $B(t) = ...
