For questions on propagation of errors.
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votes
1answer
13 views
Error Propagation in Successive Least Square Adjustment
I have a certain problem in surveying in which I'm trying to do some error analysis. I'll layout the problem first.
My current goal is to evaluate the variance-covariance matrix for the
position of ...
0
votes
1answer
16 views
What is the proper way to determine error in my measurements?
How do I know what the error is in measurements I took using an oscilloscope?
In the image below you will see on channel #1 of the oscilloscope (yellow) there is a pattern. I manually measured the ...
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0answers
27 views
What is the error in Newton's Method for Matrix Inversion?
I need it to invert a matrix. Wikipedia explains that there is a generalization of the Newton Method for matrices. However, there is nothing mentioned about the error bounds.
Suppose we have, as ...
1
vote
0answers
79 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 ...
2
votes
1answer
57 views
Absolute and Relative Error of $x^y$
Suppose that we have two measured values $x$ and $y$ with maximum absolute errors of $e_x$ and $e_y$.
Is there a formula to find a good upper bound for absolute and relative error of $x^y$?
1
vote
1answer
30 views
How to estimate (if/any) displacement/rotations between 2d line segments taken from 2 data sets
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 derive these two line sets using image based (e.g. CD) and manual method ...
1
vote
0answers
31 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 ...
0
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0answers
24 views
Measurement error influence
Let's say we have 260 daily measurements of variable X. The picture in the link shows graphically those measurements. This variable has an average measurement error of ±1 units.
I want to prove that ...
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0answers
21 views
best way to estimate deviation of 3d line segments with respect to reference segments
I have set of 3D line segments derived in two different method. These line segments represent edges of several 3d cubs and polygons.
(1) first set of line segments are derived by doing field ...
1
vote
1answer
40 views
Where does the error propagation formula comes from?
As an engineering student I have come several times across the formula $$\sigma_{f(\vec{x})}=\sqrt{\sum_{i} \big (\dfrac{\partial f}{\partial x_{i}}\sigma_{x_{i}}\big )^{2}}$$ for the propagation of ...
0
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1answer
123 views
Proving the relative error of division.
The problem says to show that the relative error for division on a computer is
$$Rel(\frac{x_{A}}{y_{A}})=\frac{Rel(x_{A})-Rel(y_{A})}{1-Rel(y_{A})}$$
$$\approx Rel(x_{A})-Rel(y_{A})$$
provided ...
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0answers
15 views
Error bounds on multiple estimate functions
I have a reciprocal square root function that is guarenteed to be accurate to within 1 part in 4096. I have a reciprocal estimate function that is also accurate to within 1 part in 4096. When I ...
2
votes
1answer
27 views
Expectation/probability question (a bit like Craps, I think)
I'll try to be as brief as possible:
I have a number of events that can happen, say e1, e2...eN. N isn't particularly large. Each event has a probability of "failure". (Actually, there will likely ...
0
votes
1answer
68 views
Error in a numerical derivative
I have a graph of data, say temperature ($T$) vs time($t$), I know the error bounds in each $\Delta T$.
The range of t is from 0 $\to$ 1600 s, with small steps say 0.001 s.
If I numerically take ...
0
votes
1answer
94 views
Angle between two vectors with noisy data?
Given two vectors V1=(x1,y1,z1) and V2=(x2,y2,z2) I can calculate the angle between the two vectors using the dot product of the two vectors and their magnitudes.
This approach, however, is only ...
1
vote
1answer
73 views
Derivation of formula for estimating error in bulk-volume
In my textbook, a formula for estimating error in bulk-volume measurements is derived, but I don't quite follow one step in the derivation. The book writes the following:
The bulk volume of a ...
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0answers
50 views
Error propagation for several variables?
I was asked this on exam today:
f(1,2)=8, f(1.01,2)=8.4, f(1,2.01)=7.8, f(1.01,2.01)=8.3 x=1±0.02,
y=2±0.03
What is the limit of error in f?
I believe it should be the error propagation ...
0
votes
1answer
86 views
errors, random and approximations
Hello good evening all!
If a reading is reported as R = 200.045 + 0.001 or 200.045 - 0.001 Ohm. Does +0.001 or -0.001 Ohm represents a systematic or random error?
Thanking you.
0
votes
1answer
34 views
Can % error in computed value be less than % error in one of its parameters
I am using an equation to compute energy as follows
$E= C_1\times t + C_2 \times a$
Here $C_1$ and $C_2$ are constants. $t$ shows the time-taken, $a$ shows the dynamic-activity.
Using a technique, ...
1
vote
1answer
299 views
Error analysis - Bisection algorithm
I have a brief question related to an example in my textbook. In my book, the following theorem on Bisection Method is presented:
If $[a_0,b_0], [a_1,b_1],. . .,[a_n,b_n]. . .$ denote the intervals ...
0
votes
1answer
218 views
Error propagation and averages, a practical question
Ok, I'm sure this is simple, yet I'm confused.
Lets say my goal is to obtain an average concentration C=N/V so I take a number of N and V readings with errors:
$N_1=50\pm2, V_1=100\pm4$
...
0
votes
1answer
36 views
I don't understand where some numbers come from when calculating the stop-and-wait frame that reaches 50% efficiency.
I am working on homework assignment and I found a similar question and the answer that I can refer to.
On this website I am being presented the question and the solution. Question 1A:
...
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2answers
1k views
Error propagation on weighted mean
I understand that, if errors are random and independent, the addition (or difference) of two measured quantities, say $x$ and $y$, is equal to the quadratic sum of the two errors. In other words, the ...
