For questions on propagation of errors.

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2answers
31 views

Order of error of a fraction

If two functions can be written as the sum of some expression and an error term of higher orders of error $\epsilon$: $$f(x+\epsilon)=f_0(x,\epsilon)+O(\epsilon^m)\quad \text{ and} \quad ...
4
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1answer
405 views

Multiplication and division of values with geometric standard deviation

What is the geometric standard deviation of a value, which is the result of dividing two independent values, each of which has its own geometric standard deviation ? It is a frequent situation in ...
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1answer
82 views

Calculating Covariance. (Multiplication of Two Covariance Matrices)

I have an equation T3=T1*T2 where T is 3*3 Transformation matrix representing position of an object in 3D. Now each of these position has some error in the form of 3*3 covariance matrix i-e ∑. My ...
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1answer
56 views

How is statistical uncertainty calculated for the modulus function?

I know it's an unusual function to calculate an uncertainty for, but I haven't been able to figure out a reasonable means for calculating derivatives for it to do so myself. I know modular arithmetic ...
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1answer
17 views

Error propagation for ratio data

I'm working with some published ratio data for isotopes of uranium (238U) and lead (208Pb and 206Pb). The data are published in ratios of 238U/208Pb and 206Pb/208Pb, but I need the data to be in the ...
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1answer
33 views

Help in Measuring Error on Estimates of Differential Equations

I am working on a project for class where I have to estimate the solutions to a damped harmonic oscillator ($x''+2 \gamma x'+ \omega^2 x=0$) and compare three methods for doing so (Third Order ...
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1answer
43 views

Error bound of the Euler method

I am self studying working through the book "A First Course in the Numerical Analysis of Differential Equations" and have come to a deadend on q 1.2. The linear system $y' = Ay, y(0) = y_0$, where ...
2
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0answers
30 views

Monte Carlo with error on individual samples

I'm performing a Monte Carlo integration where the individual samples have an error, and I'm wondering how to estimate the final error. Some more detail: The integral E I'm after is estimated in the ...
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0answers
27 views

Yacov Perelman Nepero game

This is my first question, so sorry if I'll make any mistake in using the site formatting. I found this game on a book by Yacov Perelman and I thought it could be nice to introduce Nepero number to ...
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0answers
19 views

Propagation of variance/covariance for $L_1$ Estimator with no analytic solution

This is my first question on Math Exchange so my apologies if it does not initially fit the format. I have a problem where I'd like to calculate the a-posteriori variance/covariance matrix of ...
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0answers
43 views

Finite difference method - implementation and stability

I have a PDE for a function $P(r,t)$ in spherical co-ordinates of the form $P_{t} = D(P_{rr} + (2/r)P_{r}) - a\Omega\left(\frac{P}{P + k} \right) $ where subscripts denote partial derivative with ...
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0answers
58 views

When examining global error bounds for Euler method, can I rescale the domain limits?

I'm looking at provable global error bounds of the Euler method for the first time and I was surprised to find that the bound grows exponentially in the amount of time (the domain size) propagated ...
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0answers
169 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 ...
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0answers
54 views

How to estimate error pattern of a set of line segments with respect to given reference segments (2D case)

I am having set of pair of line segments (2D). Though each pair should be coincided on top of each other they are not so. I have been the reference data and then I extracted other line segments ...
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0answers
16 views

Error propagation in pearson correlation

I have two data-sets $X$ and $Y$ with errors $\Delta X$ and $\Delta Y$. I calculated the Pearson Sample Correlation $r$. Is it possible to calculate the error of $r$ using propagation of uncertainty: ...
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0answers
13 views

How to express the quantity using significant figures to imply the stated error?

Express the quantity using significant figures to imply the stated error. $$1.77 \pm 0.06$$ I tried to factor out a $6$ and got $6(.295\pm0.01)$ but then when I try to make $.295$ have an error of ...
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0answers
10 views

How to find error constant, global and local error of ODE integration method

In literature regarding open channel flows I bumped into strange ODE integration methods: the first one: $$y_{i+1}=y_i+\Delta x\cdot\sqrt{f_i\cdot f_{i+1}}$$ the second one $$y_{i+1}=y_i+\Delta ...
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0answers
18 views

what are some good ways to define the errors between two functions?

I have two functions. One is the original function (that contains 4 variables), and the second one is the approximation to the first one (also contains 4 variables). The question is, if I want to ...
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0answers
6 views

To find error in time histogram

I have a data which is recorded from a detector. Whenever the detector produce signal it records the time. I have recorded the data for several cycles, one cycle is 0 to 1 second. Finally I made the ...
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0answers
20 views

Monte carlo error: Combining “experimental” and statistical errors

I'm doing a slightly involved Monte Carlo approximation of a quantity $E$ where I end up with the following formula: $E=\frac{\sum_{i=1}^np_ie_iG_i}{\sum_{i=1}^np_iG_i}\ .\ \ \ \ \ \ \ \ \ $ (1) ...
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0answers
11 views

looking for asymmetric probability distribution

In physics, quantities are sometimes measured with both an upper and lower error. For example, I might say that an object's mass is $m = 10^{+0.1}_{-0.2} \text{ kg}$. In my case, these arise from ...
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0answers
34 views

Standard deviation on absolute square of complex average

I am calculating a quantity $q=|c|^2$ where I obtain $c\in\boldsymbol C$ as an average of a collection of estimates with errors: $\langle c\rangle=\sum_{j=1}^nc_j$, and the question is what error to ...
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0answers
43 views

Error Propagation - functions of the mean.

Given a number of measurements $\{x_i\}$ with values distributed according to a (known) probability distribution $\rho(x)$ with a theoretical mean $\langle x\rangle = \int dx x\rho(x) = f(y)$ and a ...
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0answers
26 views

Error of the norm of solution in linear least-squares

How can we estimate the solution norm ($\Vert x \Vert$) error, separate from the solution ($x$) error in solving $Ax=y$ (linear least-squares problem)? Is the error of $\Vert x \Vert$ higher or lower ...
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0answers
68 views

Numerical Error in Computation - What Are the Students' Expected to Know?

I'm going to conduct an educational research about math undergraduates' conceptions about "numerical error." So I'm making a list of items I think someone with a BSc in mathematics is expected to know ...
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0answers
49 views

Propagation of standard deviation for random variable with Markov Property

I have a discrete random variable, $X \in \{0,1,2,3\}$. Define the indicator function: $$ 1_{k}\left(x\right) = \begin{cases} 1, & \text{if $x=k$} \\ 0, & \text{otherwise} \\ \end{cases}$$ ...
0
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0answers
60 views

Propagation of errors in non-linear function of uncorrelated variables

I have a non-linear recurrence relationship $Y$, where $\beta$ and $\sigma$ are variables from continuous distributions, à priori uncorrelated. Is there anything I can say about error propagation? ...