# Questions tagged [error-estimation]

For questions about determining the error caused by specific computational procedures, approximations, or numerical representations.

147 questions
Filter by
Sorted by
Tagged with
1k 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 ...
3k views

### Why do equi-spaced points behave badly?

Experiment description: 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. Each ...
7k views

### What are differences between 'a priori' and 'posteriori' error estimate in numerical analysis?

I have learnt about Finite Element Method (also a little on other numerical methods) but I don't know what are exactly definition of these two errors and differences between them?
2k views

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 ...
2k views

### What are the relative benefits of using Adams-Moulton over Adams-Bashforth algorithm?

I am solving a system of two coupled PDE's in two spatial dimensions and in time computationally. Since the function evaluations are expensive, I would like to use a multistep method (initialised ...
1k views

### Estimating hardware error probability

Say I run a supercomputer computation on 100k cores for 4 hours on http://www.nersc.gov/users/computational-systems/edison/configuration, exchanging about 4 PB of data over the network and performing ...
282 views

### Finite elements $W^{1,\infty}$ error estimates

Are there finite element method setups that provide error estimates in the $W^{1,\infty}$ norm (i.e., bounds on $\|u'_h - u'\|_\infty$)? Which families of elements can be used for implementing them? (...
336 views

464 views

### How can I derive the a priori error estimate for a symmetric bilinear form using lagrange finite elements?

Suppose that I'm solving the poisson equation by the finite element method by lagrange elements. I know that the error can be measured in a variety of ways, depending on which norm you choose. For a ...
3k views

254 views

2k views

### Error propagation through an FFT

If I take the Fourier transform of data $x \pm \sigma$, is there a standard approach to what the error in the outputs will be? Would the best way be a direct evaluation of the upper and lower bounds?
71 views

### Global reconstruction defined elementwise in a-posteriori error estimator

This question is a follow-up of this previous one. In "Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems" by Georgoulis et al., an error estimator is ...
141 views

### Stable computation of $\log\sum x_i$ from $\log x_i$, with many terms

Kahan's summation algorithm is a method to compute sums: $$\sum x_i$$ with many terms, without significant error. I want to do this with very large numbers, and instead of the numbers themselves, I ...
5k views

### How to avoid the round-off errors in the larger calculations?

Now I need to sum up more than one thousands of terms and then make the four-dimmensional integral in my Fortran program. I found that there are some numerical errors. Can you give me some suggestions ...
321 views

### Error of interpolating polynomial

$f(x)= \frac{1}{1+x^2}$ and when I computed the interpolating polynomial of 5 equally spaced points in [-5,5] I got $p(x)= 0.0053x^4 -0.1711x^2 +1$ Now I need to estimate the error in the ...
96 views

### Error control and sequence acceleration at the same time

In a posteriori error control for solving ODEs, one typically computes two different approximate solutions, one of which being "more accurate" and one of which being "less accurate". If $y_q^{n+1}$ is ...
252 views

### Asymptotic error of forward Euler

I'm trying to understand the asymptotic error behaviour of forward Euler (finite difference method), as timesteps are decreased (refined), so I feel trust in the method of manufactured solutions (MMS)....
286 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 ...
Related to: What are the negatives of using higher order finite diference schemes? Problem: I have some discrete data of a trajectory $x_t$ with errors $\delta x_t$ of a physical system sampled at ...
The following problem is given: $$- \bigtriangleup u = f, \quad \partial_n u = g \quad \text{on } \Gamma_N, \quad u = 0 \quad \text{on } \Gamma_D$$ with $\Gamma_N$ or $\Gamma_D$ denoting the ...