Related papers: Twofold fast summation
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…
Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…
Q-learning is a stochastic approximation version of the classic value iteration. The literature has established that Q-learning suffers from both maximization bias and slower convergence. Recently, multi-step algorithms have shown practical…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
The evaluation of clustering results is difficult, highly dependent on the evaluated data set and the perspective of the beholder. There are many different clustering quality measures, which try to provide a general measure to validate…
This paper discusses a simple and effective method for the summation of long sequences of floating point numbers. The method comprises two phases: an accumulation phase where the mantissas of the floating point numbers are added to…
We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
In this paper, we formulate a new \emph{multiple-correction method}. The goal is to accelerate the rate of convergence. In particular, we construct some sequences to approximate the Euler-Mascheroni and Landau constants, which are faster…
Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is present in many DNN software…
Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded…
In the present paper we are concerned with a numerical algorithm for the approximation of the two-dimensional neural field equation with delay. We consider three numerical examples that have been analysed before by other authors and are…
The Fast Fourier Transform (FFT), as a core computation in a wide range of scientific applications, is increasingly threatened by reliability issues. In this paper, we introduce TurboFFT, a high-performance FFT implementation equipped with…
In this paper, we present a significant improvement of Quick Hypervolume algorithm, one of the state-of-the-art algorithms for calculating exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used…
In this paper, we propose a mixed-precision convolution unit architecture which supports different integer and floating point (FP) precisions. The proposed architecture is based on low-bit inner product units and realizes higher precision…
In the first part of the paper we present a short review of applications of digital differential analyzers (DDA) to generation of circles showing that they can be treated as one-step numerical schemes. In the second part we present and…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
We investigate the approximation for computing the sum $a_1+...+a_n$ with an input of a list of nonnegative elements $a_1,..., a_n$. If all elements are in the range $[0,1]$, there is a randomized algorithm that can compute an…
A robot can invoke heterogeneous computation resources such as CPUs, cloud GPU servers, or even human computation for achieving a high-level goal. The problem of invoking an appropriate computation model so that it will successfully…
The problem is to evaluate a polynomial in several variables and its gradient at a power series truncated to some finite degree with multiple double precision arithmetic. To compensate for the cost overhead of multiple double precision and…