Questions tagged [acceleration]
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12 questions
1
vote
1
answer
72
views
Why does a two-body simulation result in no change of the y-component?
I've been attempting to create a model of a heliocentric orbit based on Newton's law of gravitation:
$$
\frac{d^2 \vec r}{dt^2} = -\frac{GM}{|r|^2} \hat r
$$
This is what I have so far:
...
- 133
0
votes
0
answers
73
views
accelerating solutions of ODEs with close by parameters
Suppose $\mathbf{u}^1\in\mathbb{R}^n$ is an unknown and $\mu^1\in\mathbb{R}$ is a known parameter. Suppose we have solved the non-linear system of equation for $\mathbf{u}^1$ using Newton's iterations....
- 852
1
vote
0
answers
61
views
Hardware supporting floats with fraction beyond 64 bit
Is there any computation accelerator (like a GPGPU) available, that natively (this means in hardware, not emulated by a library) supports arithmetics using floating point numbers with a fractional ...
- 163
2
votes
2
answers
221
views
Accelerating convergence of a generalized continued fraction
I wish to compute
$$
\frac{1}{1 + \frac{1^3}{1 + \frac{2^3}{1 + \frac{3^3}{1+\cdots} } } }
$$
to high accuracy. To start, I tried computing
$$
\frac{1}{1 + \frac{1^2}{1 + \frac{2^2}{1 + \frac{3^2}{1+\...
- 2,165
5
votes
1
answer
162
views
Accurate computation of Gauss-Kuzmin entropy
The Gauss-Kuzmin distribution gives the probability of an integer appearing as a partial denominator in the continued fraction of a real number $x$ as
$$
P(a_k = k) = -\log_2\left(1 - \frac{1}{(k+1)^2}...
- 2,165
1
vote
0
answers
28
views
Speedup of CPU Pipelining by number of steps [closed]
When a CPU has $K$ steps the speed up of using pipelining compared to non-pipelining is $K$. But what I want to know is, say I am a CPU designer and want to decide whether I should build $K$ or $N$ ...
3
votes
2
answers
120
views
Error control and sequence acceleration at the same time
In a posteriori error control for solving ODEs, one typically computes two different approximate solutions, one of which being "more accurate" and one of which being "less accurate". If $y_q^{n+1}$ is ...
- 399
2
votes
0
answers
112
views
Accelerate computation speed by using a different syntax [closed]
I was reading a book about Matlab ("Accelerating Matlab with GPU computing - A Primer with Examples" by Jung Suh and Youngming Kim, 2013. Chapter 1.7 Examples).
I read an example where it said that: ...
- 153
3
votes
0
answers
145
views
Acceleration of matrix geometric series
Suppose we want to find $x$ such that:
$$x=b+Ax$$
where $A$ is a large sparse square matrix with eigenvalues in the unit circle.
There are two representations of the solution:
1)
$$x=(I-A)^{-1}b,$$...
- 131
0
votes
1
answer
164
views
Converting acceleration over time to velocity or speed in code
I have acceleration data from a sensor. X Y & Z.
I move the senor in the Y axis. Mostly in a straight line. So I ignore x & z.
From the sensor documentation
5.2.1 Acceleration output：
ax=((...
- 101
0
votes
1
answer
65
views
Converting mass density to point mass approximation on a grid
In an nbody gravity simulation, instead of doing exact(all-pair brute force) solution, I added masses of each body into cells of a 3D grid(each cell is just a float value having a mass value). Then ...
6
votes
1
answer
215
views
Fast multiplication of highly structured matrix
I want to compute a fast matrix-vector product using a matrix $T$ which has a peculiar quasi-Hankel structure. For example,
\begin{equation}
T_2=
\left(
\begin{array}{c|ccc|cccccc}
a & b & c &...
- 1,031