All Questions
Tagged with floating-point error-propagation
8
questions
4
votes
2
answers
110
views
pow and its relative error
Investigating the floating-point implementation of the $\operatorname{pow}(x,b)=x^b$ with $x,b\in\Bbb R$ in some library implementations, I found that some pow ...
- 10.5k
1
vote
1
answer
172
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Does using smaller floating-point numbers decrease rounding errors?
I started learning about floating point by reading "What Every Computer Scientist Should know About Floating-Point Arithmetic" by David Goldberg. On page 4 he presents a proof for the ...
0
votes
1
answer
632
views
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 ...
- 1,609
1
vote
0
answers
105
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Floating point arithmetic error propagation
I have a function $$y=ln(\frac{x_1}{x_2})$$, $$x_1, x_2 > 1$$ and two ways to calculate it:
$$v = \frac{x_1}{x_2} => y_1=ln(v)$$
$$v_1 = ln(x_1)$$
$$v_2 = ln(x_2)$$
$$y_2 = v_1 - v_2$$
How ...
- 11
1
vote
0
answers
58
views
Simulations and floating point error?
Dear math stack exchange,
I'm curious about what would floating point error would look as i've been hoping to conduct some simulations of gravitational phenomenon. Is it highly random or somewhat ...
2
votes
2
answers
2k
views
Error Propagation in Floating-Point Multiplication
Wikipedia (Machine epsilon) tells me that the result of a multiplication between 2 floating-point numbers, with a rounding induced relative error ϵ, still only has the relative error ϵ.
Why do the ...
- 27
0
votes
2
answers
150
views
Derive worst case error inputs for floating addition/multiplication
It is well know the following floating point model
$$
fl(x \;op\; y) = \left( x \;op\; y \right)(1+\delta), |\delta| \leq u = 2^{-t-1}
$$
(section 2.2. formula 2.4. of this book).
Just because I ...
- 5,317
1
vote
1
answer
192
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 ...
- 5,317