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.
2
votes
2answers
90 views
Do RBF kernel matrices tend to be ill-conditioned?
I use RBF kernel function to implement one kernel based machine learning algorithm(KLPP),
the resulting kernel matrix $K$ $$K(i,j)= \exp\left({\frac{-(x_{i}-x_{j})^2}{ \sigma_{m}^2}}\right)$$
is ...
4
votes
2answers
102 views
Intermediate values (interpolation) after Runge-Kutta calculation
I have a numerical ODE simulation that I computed at fixed time step $h$ using a 4-th order Runge-Kutta method (RK4), producing a series of results $(x_1,y_1), ...
1
vote
0answers
11 views
Combining trend estimation and constrained Marquart fit
This title certainly needs some clarification: I need to compute parameters $a_i$ for a helper function $f(\vec{a};k)$ (for grid interpolation) which is fitted to a number of values $y_k$ which are ...
3
votes
1answer
82 views
Minimal surface solution in Python
Note: this question was also posted in StackOverflow and math.stackexchange.
I have a set of 3D points defining a 3D contour, as shown below. The points in this contour lie in their best-fit plane ...
2
votes
2answers
48 views
How to properly use polynomial projection to get values at visualization nodes?
I am trying to implementing a nodal discontinuous Galerkin spectral element method for linear and non-linear systems of equations. The solution at each time step is given at ...
4
votes
2answers
103 views
SciPy interpolation with Univariate Splines
I have coded a routine for interpolation with B-splines, only to discover later that this functionality is already included in Python's SciPy.
However, I do not understand one parameter in the SciPy ...
0
votes
0answers
43 views
Discrete Fourier Transform Vs. Inverse Discrete Fourier Transform (Division by Number of Samples) [closed]
I've noticed that there are two possible notations for both DFT and IDFT.
The First One
DFT:
$$
y_i = \sum_{j = 0}^{n - 1} x_j \cdot \omega_n^{i \cdot j}, i = 0, \dots, n - 1
$$
IDFT:
$$
x_i = ...
15
votes
2answers
207 views
Why do equi-spaced points behave badly?
Description of experiment:
In Lagrange interpolation, the exact equation is sampled at $N$ points (polynomial order $N - 1$) and it is interpolated at 101 points. Here $N$ is varied from 2 to 64. ...
0
votes
1answer
33 views
Clarification on interpolation equalities given by Briggs
Briggs, "A Multigrid Tutorial" (pg. 35) has the following expressed as 2-D interpolation:
\begin{align*}
v^h_{2i,2j} &= v_{i,j}^{2h}\\
v^h_{2i+1,2j} &= 0.5\cdot(v_{i,j}^{2h} + ...
2
votes
1answer
95 views
Prolongation/Restriction Operator in Multigrid
In Multigrid, using Poisson's equation, does the equality below always hold regardless of what type of boundary conditions you use?
$$
R= c\cdot I^T, \text{ for some constant }c
$$
where $R$ and $I$ ...
2
votes
1answer
37 views
Integrating from tabular data, in particular steam tables
I'd like to be able to view in graph form the volume and pressure of steam produced from heating water in a sealed vessel, starting from room temperature water.
Important variables, such as the ...
2
votes
0answers
27 views
Propogated Error in Mesh Interpolation
I am working with a code that solves diffusion/reaction equations on a 2D unstructured mesh. Due to the stiffness of some of the processes, I start with time steps near 1e-13, and end with a final ...
3
votes
1answer
115 views
restriction and interpolation in multigrid method
I need detailed explanation of the formula below
A2=I1*A1*I2
I suppose this formula computes matrix A2 on a coarse grid and here A1 is original matrix on fine ...
-1
votes
1answer
99 views
ENO/WENO vs monotone Hermite interpolation
I have see the method PCHIP in matlab that implements the monotone Hermite interpolation method which was originally proposed by Carlson in 1980s. It seem to accomplish the goal of preventing the ...
4
votes
1answer
84 views
What is the most efficient approach to interpolate values between two FEM meshes in 2D?
I am looking for efficient algorithm to interpolate values from one unstructured 2D mesh grid to another. Both grids are constructed using the same type of elements (triangles or quadrilaterals). Both ...
4
votes
1answer
183 views
Grid mapping from an unstructured triangular mesh to a regular rectangular mesh
I am modeling fracture propagation using a 2-D dynamic unstructured grid. As the fracture propagates over time, the elements move accordingly. For a given time step, I would like to interpolate the ...
5
votes
1answer
84 views
interpolation combined with methods of characteristics can cause oscillations for the transport equation?
I would like to know about the effect of using a higher order interpolator for the methods of characteristics. I am solving $$u_t+a(x,t)u_x=0$$ with some nonsmooth initial data $u_0(x)$ by the method ...
8
votes
4answers
197 views
When we use Bernstein polynomials in application
When it is preferable to use Bernstein polynomials to approximate a continuous function instead of using the only following preliminary Numerical Analysis methods: "Lagrange Polynomials", "Simple ...
1
vote
0answers
68 views
Resampling of values between body fitted and cartesian grids
Assuming there exist two 2D grids on the same domain, one of them is a cartesian one while the other is curvilinear (body fitted regular grid, with curved coordinate lines).
I am looking for a way to ...
3
votes
2answers
283 views
Piecewise polynomial interpolation: Hermite vs Lagrange
I am a bit confused of the qualitative behavior of the two methods. Consider quadratic case, start by having points $x_i$, where I know the value and points $y_j$, where the values to be found. If I ...
8
votes
1answer
229 views
Fast (approximate) evaluation of Chebyshev polynomial
Is there a preferred way how to implement a fast (approximate) evaluation of the Chebyshev interpolation polynomial on uniform grid (given the function values at the Chebyshev nodes)? My problem is ...
5
votes
2answers
184 views
Interpolation schemes to move data between cells and nodes
I work on non-graded quadtree grids where the entire grid is a hierarchy of cells specified using a quadtree data structure, where, in general, there is no constraint regarding the relative size of ...
2
votes
2answers
181 views
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 ...
8
votes
4answers
617 views
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 ...
6
votes
5answers
496 views
Interpolate 2D data
I generated a cartesian grid in Python using NumPy's linspace and meshgrid, and I obtained some data over this 2D grid from an ...
8
votes
2answers
365 views
How to interpolate multipoint data to the cell centres of an unstructured mesh?
I have sets of multipoint field data, each point data set relates to a single cell of an unstructured mesh. The goal is to interpolate the data to the cell centre, directly or indirectly, in the most ...
5
votes
4answers
1k views
High Order derivatives of splines using SciPy
I have created a spline to fit my data in python using:
spline=scipy.interpolate.UnivariateSpline(energy, fpp, k=4)
The equation I want to use involves a ...
3
votes
1answer
243 views
What is the most accurate interpolation method for a 3D-flowfield on a structured grid?
I solve multi-species, compressible Navier-Stokes equations on a 3D structured grid. I have obtained a solution on a given grid (let's say a relatively coarse one). I want now to refine my grid and ...
