# Tagged Questions

1answer
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### 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|| = ...
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 $N(f)=|f(0)|+|f’(0)|+||f''||_{\infty}$ ...
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. ...
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 ...
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  ...
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) = ...
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