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A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
Post-training quantization (PTQ) has emerged as a prevailing technique for deploying large language models (LLMs) efficiently in terms of both memory and computation, across edge devices and server platforms. Existing PTQ methods primarily…
The classical iteratively reweighted least-squares (IRLS) algorithm aims to recover an unknown signal from linear measurements by performing a sequence of weighted least squares problems, where the weights are recursively updated at each…
This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
The common method to estimate an unknown integer parameter vector in a linear model is to solve an integer least squares (ILS) problem. A typical approach to solving an ILS problem is sphere decoding. To make a sphere decoder faster, the…
Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
The polysymplectic analysis of the Short Pulse Equation known in nonlinear optics is used in order to construct a geometric polysymplectic integrator for it. The proposed scheme turns out to be much more effective than other standard…
We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…
NISQ (Noisy, Intermediate-Scale Quantum) computing requires error mitigation to achieve meaningful computation. Our compilation tool development focuses on the fact that the error rates of individual qubits are not equal, with a goal of…
Information retrieval (IR) systems play a critical role in navigating information overload across various applications. Existing IR benchmarks primarily focus on simple queries that are semantically analogous to single- and multi-hop…
An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
This document contains notes based on lectures given by Hendrik Lenstra at the PCMI summer school 2022. There are many problems in algebraic number theory which one would like to solve algorithmically, for example computation of the maximal…
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…
The paper reports on a computer algebra program LSSS (Linear Selective Systems Solver) for solving linear algebraic systems with rational coefficients. The program is especially efficient for very large sparse systems that have a solution…
The solution of large, sparse constrained least-squares problems is a staple in scientific and engineering applications. However, currently available codes for such problems are proprietary or based on MATLAB. We announce a freely available…
In this paper, two Q-learning (QL) methods are proposed and their convergence theories are established for addressing the model-free optimal control problem of general nonlinear continuous-time systems. By introducing the Q-function for…