Tagged Questions

For questions on propagation of errors.

21 views

What should be the expected error of a 4th order Runge-Kutta integration in a multivariable (non-linear) context?

I am writing a program where the user input $n$ variables, their initial values and differential equations. They may be non-linear. To find the value of the variables at a time $(t_0 + T)$, I use 4th ...
29 views

Error propagation - implicit functions

I have a little problem that I should solve quickly and I'm a little bit on pressure, so that any help/tip would be of great help. I have two nonlinear equations with two unknown variables x and y ...
24 views

Significance and Poisson processes

Must I include the Poisson error on a new observation when considering whether it is consistent with a distribution? For example, the number of rain drops that fall into a cup per minute are recorded....
19 views

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 ...
8 views

How to make a covariance matrix from multiple observations of different objects?

I have $N$ objects. From each object, I sample $M$ values $(x,y)$ like so: ...
34 views

Calculating a three sigma limit on data

So I have a list of data points each with their own error (eg. 3 +/- 0.2 units) and I want to determine which of the data points are within 3 sigma. To do this do I just calculate the standard ...
10 views

Input Error estimation

I was wondering what are the methods used to detect the input's error when having the output's error of a model. I thoroughly searched on google, but I failed to find a well explined method, or ...
18 views

26 views

21 views

Uncertainty propagation and division

I am getting confused about a super basic issue. I have two quantities: $6\pm4$ and $4\pm3$ . So let's say $x = 6$, $\Delta x = 4$, $y = 4$, $\Delta y = 3$ Now I want to calculate the uncertainty ...
37 views

Error in average of $x^2$ from error in average of $x$?

Is there an easy way to obtain the error in $\langle{x^2}\rangle$ from $\langle{x}\rangle$ or are they independent? The values of x are from a molecular simulation application, I obtained a set of ...
25 views

How should I compensate for numerical inaccuracy in fixed-point multiplication?

I am experimenting with fixed point arithmetic. I found a library for doing fixed-point math using vectors of 32-bit integers . At the end of the mulfpu (unsigned fixed point multiplication) ...
36 views

28 views

The area of a triangle ABC is given by S = 0.5abSin(C) calculate the max percentage error of S

$S=0.5abSin(c)$ calculate the maximum percentage error of S when a,b and c have a percentage error within 1% and c = 45 degrees. I do not understand where I went wrong the answer is supposed to 2.8%. ...
18 views

Error propagation: add errors in quadrature, or use a weighted standard deviation?

I have a measurement $x$ with a known uncertainty $\sigma_m$. I have a black box that can take an error-free measurement $x$ and produce a value $y$ with a known uncertainty $\sigma_{b}$ (which is ...
39 views

17 views

What are disadvantages of solving difference equations backwards?

Say you have the initial value of 100th and 99th term and you want to see how much error is in 1st term instead of picking values from the table for 1st and 2nd term and propagating to 99th and 100th ...
21 views

error calculation when the error is not constant

I have to calculate the error on the following quantity: $$f(\epsilon^M,\epsilon^S)= \sqrt{ \frac{1}{N}\sum_{i=1}^N (\log{\epsilon_i^M} - \log{\epsilon_i^S})^2 }$$ Usually I would use this standard ...
25 views

73 views

Find the absolute and relative error for a calculator with incorrect rounding

A calculator is out of order. The calculator will round up every single number to the nearest integer if the value at the first decimal digit is 6 and above, or else it rounds down the number to be ...