# Questions tagged [error-estimation]

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### Correct relative error for Comparison of levelsets outside a constrained region

I am working on the estimation of tumor extent outside of the region which is visible in MRT/CT/DTI images. I want to compare two methods, which approximate the tumor density profile. Lets say the ...
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### Offline Parameter Estimation for second order system - Ordinary Least Squares

I have a second order system which is described by the following differential equation: $\ \ddot{y}+α_{1}*\dot{y}=b_{0}*u$ where $\ y$ is the output of the system and $\ u$ is the input of the ...
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### The proper way to assess the error of Jacobi iteration (for 2D Poisson equation)?

Motivation: I'm using 2D regular grid (it's actually a quadtree but I can still treat it as a finite difference thing if I weight-average the solution over smaller scale cells for the purpose of ...
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### Cubature rule in unit Sphere in $\mathbb{R}^{3}$

I need to find the cubature rule for the following integration $$\int_{S^{2}} f(s,\tilde{s})d\tilde{s} ds,$$ where $S^2$ is the unit sphere in $\mathbb{R}^{3}$.
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### Error on a integral quantity with noise

First of all sorry if this is the wrong place to ask this question, I went to a few stack sites and thought here it would be more suitable. My problem: I have a physical quantity $F$ that depends on ...
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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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### Stabilizing online average calculation

In Knuth, the following method for computing an average is presented: \begin{align*} M_{n} = M_{n-1} + (x_{n} - M_{n-1})/n \end{align*} (See here, if you don't have TAOCP.) Assuming the samples all ...
In some of my computations I calculate a scalar value $\lambda_h$ (in my case an eigenvalue) depending on a finite element discretization of the domain. Usually we can manage to find estimates of the ...