Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [interpolation]

Interpolation is the process of estimating the values of a function, when the function's values are known only at a particular set of points. Questions on interpolation in one or more dimensions, as well as algorithms for doing so, should have this tag.

196 questions
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Example of a continuous function that is difficult to approximate with polynomials

For teaching purposes I'd need a continuous function of a single variable that is "difficult" to approximate with polynomials, i.e. one would need very high powers in a power series to "fit" this function well. I intend to show my students the…
András Aszódi
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4 answers

Efficient interpolation method for unstructured grids?

I would like to know a good method for interpolating data between two unstructured grids, where one grid is a coarser version of the other. Efficiency is very important to me since I'm solving a transient PDE problem where I need to transfer data…
Bernardo M. R.
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Polynomial interpolation on a regular hexagon

Background We know a function $f$ on the vertices of a regular hexagon, as follows $$\left( 1, \ 0, \ f_{0}\right), \ \left( \frac{1}{2}, \ \frac{\sqrt{3}}{2}, \ f_{1}\right), \ \left( - \frac{1}{2}, \ \frac{\sqrt{3}}{2}, \ f_{2}\right), \ …
nicoguaro
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Adaptive Table Lookup for Expensive Function Evaluation

I have a function that is expensive to evaluate whose inputs are n-dimensional (n is the order of a dozen or two). I need the output of this function at each node and each time step for a PDE simulation. I know that the portion of the n-d space…
Godric Seer
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1 answer

Surface interpolation from two lines

Sorry if this is a basic problem but I don't know where to start looking (mainly because being an outsider I don't know the terms and nomenclature). Imagine two perpendicular lines ("profiles") in a "T" spatial arrangement. The lines are arbitrary…
terauser
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Interpolate the orbital coordinates of an object using coordinates and velocities vector

I have a table of the orbital coordinates and velocities of an object with time steps of 1 minute. Now I would like to interpolate this to a finer time increments with time steps of the order of 1 second. How to make use of the velocities in…
Tarlan Mammadzada
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Why weighted harmonic mean for pchip slopes leads to monotone interpolator

In Fritsch and Carlson's paper on monotone interpolation, they identify numerous conditions under which a cubic Hermite interpolator will be monotone. For example: On the subinterval $[t_i, t_{i+1}]$ where $p(t_i) = y_i$ and $p(t_{i+1}) = y_{i+1}$,…
user14717
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At which stage to interpolate?

Assume I have a multidimensional grid $G$. I consider two functions $f(x)$ and $g(x)$. I have solved the values for the functions over all grid points $x \in G$. Let me now be interested in some third function $F(f(x),g(x))$. I am looking to…
fes
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1D irregular interpolation with $O(1)$ or $O(\log(N))$ evaluation

In Floater's paper on barycentric rational interpolation, he shows that a stable interpolant using irregularly space points can be evaluated in $O(N)$ operations. For equally spaces samples, cubic b-splines can be used to generate an interpolator…
user14717
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Methods for interpolating from points that are not on a regular grid?

I'm working on a project where I'll need to be able to interpolate scalar potential values at arbitrary points in a 3-D box from a large (potentially millions to billions of points) collection of values that were calculated at points of convenience…
Brian Borchers
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L2-Projection using quadratic basis functions

I am trying to understand 1D $L^2$-projections using quadratic basis functions. Using 3 data points, and the Lagrange polynomial it is easy enough to see how to write out 3 basis functions. With the hat functions from the linear basis, it is easy to…
wgwz
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error of linear interpolation

I have two points $x_1, x_2$ between which I would like to have a linear interpolation $P_1$. Those two points are just points where I know the value of the underlying function $f$. I know that the error at any point between the two will be bounded…
Kamil
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trigonometric interpolation with non-equidistant sampling

I want to interpolate a periodic function on a non-equidistant grid and have implemented it the using the Lagrangian formula described in wikipedia. For an odd number of data points, this takes the form $$p(x) = \sum_{k=0}^{2K}…
Toon
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How do I do Chebyshev interpolation in multi-dimentional space?

This topic is used in spectral methods, for collocation grid. Literature mentions Chebyshev interpolation on a grid (defined by $\xi_j = cos(\pi \cdot j/N)$, $x_j = (\xi_j+1) L/2$, $j=0,...,N$) includes 2 steps 1/ Calculation of Chebyshev…
user5273
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1 answer

Monotonicity preserving interpolant in 1D

I have a dataset $\{x_i, y_i\}_{i=0}^{n-1}$ where $x_0 < x_1 < \cdots x_{n-1}$ (not uniformly spaced), and, in addition $y_0 < y_1 < \cdots y_{n-1}$. So it feels natural to assume that $y_i$ are samples of an unknown monotonically increasing…
user14717
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