# Questions tagged [error-estimation]

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### Numerical analysis: Chebyshev coefficient representation error

If $x_k$ are the Chebyshev nodes, that is for $n \in \mathbb{N}^*$, we have $x_k = \cos(\pi \frac{2k + 1}{n})$. Now suppose you have approximated values of $x_k$ and $x_{k'}$ for $k,k' \leq n$. In the ...
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### Procedure to identify characteristic properties of unknown functions in a DAE model

I have a system of 1st order odes given by $$\dot{x_1}(t) = \alpha_1 f_1(x_1,t) + \beta_1 u(t) \\ \dot{x_2}(t) = \alpha_2 f_2(x_2,t) + \beta_2 u(t)$$ They are constrained by an algebraic equation ...
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### Round-off errors in ratio of Gaussian functions

I would like to understand how division of round-off errors can lead to large errors??? I am using a method to measure the frequency dependent dissipation in simulations performed by Discontinuous ...
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### How group similar data in a single classes and reduce the error

I have vehicles gps information in my real time traffic application. Averaging that information I know the speed of every road at any time. The problem is that is too much data to send back to the ...
236 views

### Estimate $L_2$ norm of a elliptic problem with unknown exact solution on finite element method

I have the elliptic problem $$-\Delta u = 1,\,\,\Omega\subset\mathbb{R}^2$$ with $u=0$ on $\partial\Omega,$ with $\Omega=[-1,1]^2\backslash([0,1]\times[-1,0])$ and I want to estimate the $L_2$ error ...
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### Square error estimate for adaptive mesh refinement

In a particular implementation(Finite volume advection using upwind) of adaptive mesh refinement the error square estimate for a cell C is given as  \sum_{i = x,y,z} vol * \frac{1}{12} * h^{2} * (\...
33 views

### Gradient convergence on a checkerboard domain in finite element

I've got an elliptic problem in a domain with two materials in a checkerboard arrangement. Both materials are highly dissimilar, being one much more compliant than the other. If I use classic linear ...
59 views

### Error in Monte Carlo integration

I am looking for a concise description to help me understand the error for Monte Carlo Integration using Uniform Sampling and Importance Sampling For Importance Sampling I have that the error is just ...
Lets say we have two things as input, $N$ scalars (measurements) that we know are erroneous to some degree (i.e. the correct values are somewhat similar). In addition, we also have a roughly more ...