Questions tagged [acceleration]

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50 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 ...
2
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1answer
68 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+\...
5
votes
1answer
144 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}...
1
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0answers
21 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
2answers
94 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 ...
2
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0answers
108 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: ...
2
votes
0answers
87 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) $$x=(I-A)^{-1}b,$$...
0
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1answer
66 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=((...
0
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1answer
35 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
1answer
189 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 &...