Related papers: Twofold fast arithmetic
Asynchronous iterative methods tolerate straggling processors by allowing workers to proceed with stale data, but at a cost: the iterates become inconsistent, potentially degrading convergence. We investigate whether convergence…
We provide a template to derive convergence rates for the following popular versions of the Frank-Wolfe algorithm on polytopes: vanilla Frank-Wolfe, Frank-Wolfe with away steps, Frank-Wolfe with blended pairwise steps, and Frank-Wolfe with…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard…
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 this paper I consider the applications of several kinds of approximations of real functions to the problem of verified computation (reliable computing) of the range of implicitly defined real function $x_{n+1} = G(x_{1}, ..., x_{n}),$…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of…
This paper describes a systematic method of numerically computing and indexing fixed points of $z^{z^w}$ for fixed $z$ or equivalently, the roots of $T_2(w;z)=w-z^{z^w}$. The roots are computed using a modified version of fixed-point…
Nowadays, locating software components responsible for observed failures is one of the most expensive and error-prone tasks in the software development process. To improve the debugging process efficiency, some effort was already made to…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
Multiple-precision floating-point branch-free algorithms can significantly accelerate multi-component arithmetic implemented by combining hardware-based binary64 and binary32, particularly for triple- and quadruple-precision computations.…
We present a simple but efficient method of calculating Stieltjes constants at a very high level of precision, up to about 80000 significant digits. This method is based on the hypergeometric-like expansion for the Riemann zeta function…
We show how to increase the accuracy of estimates of the two-point correlation function without sacrificing efficiency. We quantify the error of the pair-counts and of the Landy-Szalay estimator by comparing them with exact reference…
A number of automated techniques and tools were proposed in the research literature over the years which aim to support the spreadsheet developer in the process of testing and debugging a faulty spreadsheet. One underlying assumption of…
Automated techniques for rigorous floating-point round-off error analysis are important in areas including formal verification of correctness and precision tuning. Existing tools and techniques, while providing tight bounds, fail to analyze…
Approximate computing (AC) is an emerging paradigm for energy-efficient computation. The basic idea of AC is to sacrifice high precision for low energy by allowing for hardware which only carries out "approximately correct" calculations.…
Some recent processors are not equipped with an integer division unit. Compilers then implement division by a call to a special function supplied by the processor designers, which implements division by a loop producing one bit of quotient…
This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and…