The error-estimation tag has no wiki summary.
6
votes
1answer
58 views
Bounding the relative error of derivative given relative error of the function
Suppose a function $f$ can be computed such that the bound on the relative error is $R$ i.e. $f^-(x) = f(x)(1+r)$ where $f^-$ and $f$ are respectively the
computed and exact value $f$ and $|r| \leq ...
1
vote
1answer
54 views
How can I quantify the error of FFT-based poisson solvers?
I have an FFT code that solves a particular case of the steady Euler equations where a Poisson equation is solved, what is a good way to quantify the error? Is what I am doing ok?
Since I do not have ...
2
votes
2answers
127 views
Problem Condition and Algorithm Stability
Consider 2 mathematical problems:
$$
f_1(x) = a - x \\
f_2(x) = e^x -1
$$
The condition number for a function is defined as follows:
$$
k(f) = \left| x \cdot \frac{f'}{f} \right|
$$
Lets analyze ...
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. ...
1
vote
1answer
66 views
Error analysis of WENO scheme
I have three questions regarding WENO schemes
1) How to actually compute the smoothness indicators $\beta_j$ for required order of polynomial? Any reference which explains the algorithm will be ...
11
votes
3answers
179 views
Numeric Quadrature with Derivatives
Most numerical methods for quadrature treat the integrand as a black-box function. What if we have more information? In particular, what benefit, if any, can we derive from knowing the first few ...
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 ...
2
votes
1answer
93 views
Diffusion-Transport problem FEM
I was looking at a book of FEM on problems of Diffusion-Transport.
$$-div(\mu \nabla u) + b \cdot \nabla u + \gamma u = f \qquad in~\Omega$$
$$u = 0 \qquad in~\partial\Omega\text{ (in the ...
29
votes
4answers
644 views
Scientific standards for numerical errors
In my field of research the specification of experimental errors is commonly accepted and publications which fail to provide them are highly criticized. At the same time I often find that results of ...
5
votes
1answer
79 views
a priori error analysis of cell-centered finite-volume methods
I'm using the cell-centered finite-volume method (for example Morton, Numerical solution of convection-diffusion problems, Chapman&Hall, 1996) to discretize the advection-diffusion equation and ...
2
votes
0answers
64 views
function over conditional probability
I need to create a scoring model out of estimated conditional probability functions for two events, A and B. Let 0.5 be the threshold value. Ideally, the probability is in the interval $[0,0.5)$ for A ...
1
vote
1answer
149 views
How to find the number of principal components that lead to the smallest generalization error?
I am working on a paper part of which is the application of validation rules to find how many principal components give us the least generalization error.
The concept goes more or less like this: ...
5
votes
2answers
370 views
When to stop Gauss-Seidel-iterations?
I want to have an estimation, that my solution has an error, let's say less than 1e-8.
Usually, I stop the Gauss-Seidel algorithm, when the residual is "small enough" and this is already the problem. ...
4
votes
3answers
233 views
What norm to choose when?
Recently, I saw this question: how to measure the error of a finite difference method
I am student of simulation sciences and unfortunately, for me, it's totally unclear, what norm to use in what ...
3
votes
1answer
96 views
Integral average approximation and error bounds
I'm looking into integrals of the form:
$$\int_a^b {f(x)g(x)dx}$$
Where $f(x)$ is unknown, but it's integral is:
$$\int_a^b {f(x)dx}=F$$
It's been suggested to me that one could approximate this ...
9
votes
2answers
148 views
What about this simple error estimate for linear PDE?
Let $\Omega$ be a convex polygonally bounded Lipschitz domain in $\mathbb R^2$, let $f \in L^2(\Omega)$.
Then the solution of the Dirichlet problem $\Delta u = f$ in $\Omega$, $\operatorname{trace} u ...
4
votes
1answer
133 views
finite difference methods and global error
I was going through my notes on different finite difference methods and came across something I don't quite understand. I have code that will calculate an approximate solution we can call this ...
