# Questions tagged [error-propagation]

For questions on propagation of errors.

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### What's best, to take the average of 2 measures or the square root of their product (in this case)?

I have a physical system where a real and positive quantity A can be measured by two ratios between 4 measures, $\frac{B}{C}$ and $\frac{D}{E}$ (all of them are positive real numbers). From the ...
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### Farmer wants to know how wet their field is

Problem A farmer wants a better understanding of rainfall on their field. Assuming rain falls randomly and with equal likelihood over the entire field, the farmer thinks they can model the volume of ...
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### Statistical method for assessing experimental and theoretical errors.

Let us suppose I have performed an experiment where the mean value is given by $V^{\rm exp}$ and its std is estimated as $\sigma_{V^{\rm exp}}$. Now, let us also suppose that theoretically, I am ...
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### Group of perfect Hamming codes

I read that a group of perfect Hamming code is defined as $[2^r-1,2^r-r-1,3]$ for any integer $r\geq 2$. To be perfect such codes should satisfy the following equivalence (derived from the Hamming ...
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### Finding roots of the equation $x^2−40x+1=0$ [closed]

The problem: Given the equation $x^2−40x+1=0$, find its roots to five significant digits. Use $√399≐19.975$, correctly rounded to five digits. Can anyone help me solve this problem? My thoughts: ...
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### Differentiation for error propagation

I am computing a quantity, $y$, from a series of measurements, $x$, made over time. The relationship is: \begin{equation} y=c\frac{dx}{dt}(b-x)^{-1} \end{equation} I would like to compute the effect ...
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### Upper bound for the error of the gaussian quadrature$\int_{0}^{1} \log (1+\operatorname{sin} x) \mathrm{d} x$

I'm given the integral $\mathrm{I}=\int_{0}^{1} \log (1+\operatorname{sin} x) \mathrm{d} x$. Through the formula of Gaussian quadrature for 3 points, I can find an approximation to this integral. The ...
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### Error in first derivative of cubic spline interpolant

Let $f: [a,b] \rightarrow \mathbb{R}$ be a $C^{\infty}$ function, and let $a = x_0 < x_1 < \cdots < x_n = b$ be a partition of the interval $[a,b]$. Let $s(x)$ be a piecewise polynomial ...
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### combining two fit results

I have got two different kind of data points $(x_i, y_i)$. Because one kind are the result of several measurements of the same object I know their statistical error $\Delta x_i, \Delta y_i$ for $x_i$ ...
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### What is the meaning of $1$ in a relative error?

If we measure a length and is measured as $12.5$ meters long, accurate to $0.1$ of a meter this means the absolute error is $0.05$m. The relative error is: $\frac{0.05}{12.5} = 0.004$. This means that ...
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### Error propagation on a 5 order polynomial

I have a 5 order polynomial equation which gives log of a chi factor required to convert equivalent widths to normalised H alpha luminosity for M dwarfs, (Reiners et al. 2008). I would like to get the ...
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### uncertainty, error propagation, residuals and least squares.

I'm stuck with something, I haven't found a proper discussion about it. Say you have a set of data $\sum_i^n (x_i, y\pm \sigma_i)$ which follows a linear trend, where there's an uncertainty $\sigma_i$...
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Question 1: I have recently tried out answering a couple of questions with the method of using the same variable in the argument of a function and a sum for example: $$\int_0^N (\sqrt{x+1}-\sqrt x)^n ... -1 votes 1 answer 299 views ### Error on the Bin of a Normalised Histogram Suppose I have a histogram, N, each with bins of width \Delta x, denoted by bin indices, i. The count of a single bin is then N_{i}. I wish to estimate the empirical density for a certain bin. ... 1 vote 0 answers 55 views ### How is SVD better than Gaussian elimination in finding the rank of a matrix? In Linear Algebra and its Applications, Gilbert Strang, 4^{th} ed, one of the applications of SVD is mentioned as finding the effective rank of a matrix. The idea presented in the book is that the ... 1 vote 0 answers 13 views ### Backward Error Analysis : Determining Errors on Model's Inputs with Known Output Errors I have an algorithm that takes 5 input parameters r, i, \Omega, \omega, f and returns two outputs X and Y. I happen to know the errors \Delta X, \Delta Y associated to X and Y (which ... 0 votes 1 answer 25 views ### Count users with big space between pings logic please try to be lenient with me because I really have forgotten most of the stuff, so I will probably be making incorrect assumptions, word the problem incorrectly, etc. Context I'm trying to ... 2 votes 0 answers 36 views ### Error Propagation on Orbital Elements through Non Linear Relation I'm having a hard time trying to propagate errors for my current work. I have two known positions X and Y that depend on several orbital parameters r, i, \Omega, \omega, f (r is a distance ... 1 vote 1 answer 37 views ### How to relate |\delta x| and |\tilde\delta x| in an inequality A\le |\tilde\delta x|\le B where A and B contain |\delta x|? |\delta x| = |(\tilde x - x)/x| (this is the absolute value of relative error) |\tilde\delta x| = |(\tilde x - x)/\tilde x| (bound for some distinct quantity) I need to find an inequality which ... 0 votes 2 answers 80 views ### Error propagation of a variable for an integral I have an integral that depends on two parameters a\pm\delta a and b\pm \delta b. I am doing this integral numerically and no python function can calculate the integral with uncertainties. So I ... 0 votes 1 answer 46 views ### derivate is based on addition, is there a muliplication analogon? like$$ \operatorname{f^o}(x) = \lim_{h\to 1} \frac{f(x*h)}{f(x)}  \operatorname{f}(x)=e^x  \operatorname{f^o}(x) = \lim_{h \to 1} e^{x*h}/e^{x} = \lim_{h\to 1} e^{x*h-x}=e^0=1  does it ...
I need to solve the following equation (for $x$): \begin{equation} \mathcal f(x):=\sum_{i=1}^n b_i \left( \frac{a_i}{1+b_i x}\right)^2-\phi=0, \quad \text{with} \quad -1/b_1< x \le 0. \end{...