Related papers: Note on improvement precision of recursive functio…
We present a new simple method for rounding a semidefinite programming relaxation of a constraint satisfaction problem. We apply it to the problem of approximate angular synchronization. Specifically, we are given directed distances on a…
We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…
Many interesting functions arising in applications map into Riemannian manifolds. We present an algorithm, using the manifold exponential and logarithm, for approximating such functions. Our approach extends approximation techniques for…
We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…
We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular,…
This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that…
This article investigates the interplay of rounding objective coefficients in binary programs and almost symmetries. Empirically, reducing the number of significant bits through rounding often leads to instances that are easier to solve.…
We present a new approximation technique for quantum field theory. The standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In a…
We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our…
The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference (qd) algorithm can be numerically unstable. The Compqd algorithm…
Random Fourier Features (RFF) is among the most popular and broadly applicable approaches for scaling up kernel methods. In essence, RFF allows the user to avoid costly computations on a large kernel matrix via a fast randomized…
In this work, we consider error detection via simulation for reversible circuit architectures. We rigorously prove that reversibility augments the performance of this simple error detection protocol to a considerable degree. A single…
We study the convergence of the shuffling gradient method, a popular algorithm employed to minimize the finite-sum function with regularization, in which functions are passed to apply (Proximal) Gradient Descent (GD) one by one whose order…
We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack,…
We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target…
Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of…
Floating-point addition on a finite-precision machine is not associative, so not all mathematically equivalent summations are computationally equivalent. Making this assumption can lead to numerical error in computations. Proper ordering…
Compression of floating-point data will play an important role in high-performance computing as data bandwidth and storage become dominant costs. Lossy compression of floating-point data is powerful, but theoretical results are needed to…
We revisit the unrelated machine scheduling problem with the weighted completion time objective. It is known that independent rounding achieves a 1.5 approximation for the problem, and many prior algorithms improve upon this ratio by…
Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. In many domains, roundoff errors are not the only source of inaccuracy…