Related papers: Computationally Inequivalent Summations and Their …
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…
Fusing sentences containing disparate content is a remarkable human ability that helps create informative and succinct summaries. Such a simple task for humans has remained challenging for modern abstractive summarizers, substantially…
Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
The paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with introduction of new concepts like the smoothing operator and semi-harmonic…
Sums-of-squares formulas over the integers have been studied extensively using their equivalence to consistently signed intercalate matrices. This representation, combined with combinatorial arguments, has been used to produce…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
What is called "numerical reproducibility" is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing…
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce…
Traditional optimization methods rely on the use of single-precision floating point arithmetic, which can be costly in terms of memory size and computing power. However, mixed precision optimization techniques leverage the use of both…
Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
The notion of comparison between system runs is fundamental in formal verification. This concept is implicitly present in the verification of qualitative systems, and is more pronounced in the verification of quantitative systems. In this…
In this paper, we address the problem of searching for semantically similar images from a large database. We present a compact coding approach, supervised quantization. Our approach simultaneously learns feature selection that linearly…
Iterative solvers are frequently used in scientific applications and engineering computations. However, the memory-bound Sparse Matrix-Vector (SpMV) kernel computation hinders the efficiency of iterative algorithms. As modern hardware…
We derive two probabilistic bounds for the relative forward error in the floating point summation of $n$ real numbers, by representing the roundoffs as independent, zero-mean, bounded random variables. The first probabilistic bound is based…
Computational models in chemistry rely on a number of approximations. The effect of such approximations on observables derived from them is often unpredictable. Therefore, it is challenging to quantify the uncertainty of a computational…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…