Questions tagged [error-propagation]
For questions on propagation of errors.
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Local vs global truncation error
I was reading about local and global truncation error, and, I must be honest, I'm not really getting the idea of the two and what's the difference.
Lets focus on the forward Euler method in ...
user168764
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Loss of significance in $a-b$
When we have two given numbers $a$ and $b$ ,if $a$ is really close to $b$,when performing $ a - b$ , we lose many significant figures,and the relative error gets really big.
But why care about the ...
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Rounding error of trapezoidal method
I'm working with the Modified Euler method sometimes called Heun's method or explicit trapezoidal method. I have a book on ordinary differential equations numerical analysis that claims:
The effect ...
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Discrepancy in value of $\int_0^\frac\pi2 \delta(\tan(t)-xt)dt$
The goal would have been for the smallest positive solution of $y\cot(y)=x$ using a Dirac $\delta(x)$ Fourier series and the Bateman function:
$$y\cot(y)=x\mathop\implies^?\frac1{\sec^2(y)-x}=\int_0^\...
- 12.1k
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1
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Error propagation, why use variences?
I have been reading up on error propagation and am slightly confused about something.
We can the error in $c=f(a,b)$ as the:
$$\sigma(c)= f_a \sigma_a+f_b \sigma _b$$
Firstly is this correct and am I ...
2
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1
answer
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Find variance of random variable $W\cos\theta+L\sin\theta$ where $L,W,\theta$ are normal random variables. Uncertainty propagation problem.
I have three variables - these are length ($L$), width ($W$) and angle ($\theta$).
Each has a known mean and variance. $\theta$ is independent, but $L$ and $W$ are correlated, and I know their ...
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Simpson's Rule for IVP. Truncation Error proof
Edit: replaced all c's with y's as the c just denotes replacing a series of coupled linear equations Ay with uncoupled equations $\Lambda c$ no biggie.
Im working through the lecture notes for a ...
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What does it mean to calculate a number to $n$ decimals of exactness.
I was asked to numerically calculate Bessel functions for certain points and report their values to "6 decimal places of exactness". I did this in matlab and there's no truncate function, so I was ...
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Is $\approx$ an equivalence relation? If $\approx$ is transitive, then does the error inherent in the approximation accumulate?
I was doing some physics calculations that involved approximations such as the small-angle approximation. I then started to wonder about how the relation $\approx$ can be used in comparison to the ...
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Propagation of error for an integral using Leibnitz' rule
I'm computing integrals $u_i$, where
$$u_i = \int_a^b s^i G(s) ds$$
and $a$ and $b$ are constants.
Now I want to estimate the error in $u_i$; I have estimates for the error $\sigma_G$ of $G$, and ...
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How can I simulate uncertainty propagation
I am learning about uncertainty propagation, but it is all very obscure and I am not sure I understand it very well.
I have a couple of exercises, but I want to run some simulations just to make sure ...
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Calculating Covariance. (Multiplication of Two Covariance Matrices)
I have an equation
T3=T1*T2
where T is 3*3 Transformation matrix representing position of an object in 3D.
Now each of these position has some error in the form of 3*3 covariance matrix i-e ∑.
My ...
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Inverse Propagation of Uncertainty
Can any one help me find a reference under the title of " Inverse Propagation of Uncertainty". I am starting a research on this topic after I had studied the forward propagation of uncertainty.
...
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Calculate uncertainty of sine function result
I have an angle given in degrees:
$$\theta_{\min} = 63^{\circ} \pm 0.5^{\circ}$$
I need to calculate it's sine and still know the uncertainty of the value:
$$n = 2\sin(\theta_{\min}) = 1....
- 353
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Minimum error in floating point approximation of an elementary function.
I need a confirmation of a thing that probably is silly.
Let $x$ a floating point number representable using $e$ bits for exponent and $m$ bits for mantissa, let $f$ a be an elementary function, you ...
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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 g(x+\epsilon)...
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Proving the relative error of division.
The problem says to show that the relative error for division on a computer is
\begin{align}\textrm{Rel}\left(\frac{x_{A}}{y_{A}}\right)&=\frac{\textrm{Rel}(x_{A})-\textrm{Rel}(y_{A})}{1-\textrm{...
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