Questions tagged [interpolation]

Questions on interpolation, the estimation of the value of a function from given input, based on the values of the function at known points. It is necessary because in science and engineering we often need to deal with discrete experimental data.

1,786 questions
Filter by
Sorted by
Tagged with
10 views

Determine spline coefficients by linear interpolation between 2 other splines

I am looking for a way to calculate a spline function from 2 previously calculated spline functions by linear interpolation. I have these functions (590.33, 911.4, 1192.51 -> linear interpolation ...
22 views

32 views

How are interpolation operators derived for multigrid

I am trying to construct transfer operators $I^H_h, \, I^h_H$ for multigrid where $H \ne 2h$. I have gone through Briggs' tutorial, Hemker's paper, Hackbush's book, Trottenberg's book, but the details ...
29 views

39 views

Range $u_{\mathrm{max}}-u_{\mathrm{min}}$ of the solution to graph Poisson equation $Lu=b$

I found out an interesting phenomenon when trying to solve the linear equation $Lu=b$, and I don't know how to interpret such phenomenon. Goal: Fit $u(x, y)=\cos(x)$ for $x,y \in [0,\pi]$. We draw ...
28 views

Help find any information about strange trigonometric interpolation

I need to find any information about this interpolation method. It is labeled "trigonometric interpolation" and is placed in the chapter "Hermite interpolation". My final goal is ...
17 views

Error in first derivative of cubic spline interpolant

Let $f: [a,b] \rightarrow \mathbb{R}$ be a $C^{\infty}$ function, and let $a = x_0 < x_1 < \cdots < x_n = b$ be a partition of the interval $[a,b]$. Let $s(x)$ be a piecewise polynomial ...
20 views

26 views

Is there a name for a set of linear functionals $f_i$ that is "sufficiently rich" to uniquely identify a polynomial from the values $f_i p$
I have found this statement in some old lecture notes on interpolation in my lab. Let $\mathcal{P}_{n}(I)$ be the vector space of polynomials over some open interval $I\subset\mathbb{R}$. Suppose some ...