Related papers: Combining Tools for Optimization and Analysis of F…
Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks…
The typical processors used for scientific computing have fixed-width data-paths. This implies that mathematical libraries were specifically developed to target each of these fixed precisions (binary16, binary32, binary64). However, to…
The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, present new opportunities for hybrid-optimization algorithms that are hardware accelerated by…
Significant inaccuracy often occurs during the process of mathematical calculation due to the digit limitation of floating point, which may lead to catastrophic loss. Normally, people believe that adjustment of floating-point precision is…
Challenges of enhancing productivity by amplifying efficiency and man-machine compatibility of equipment can be achieved by adopting advanced technologies. This study aims to present and exemplify methodology for incorporating ergonomics…
Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may differ from the…
Collaborative filtering is an important technique for recommendation. Whereas it has been repeatedly shown to be effective in previous work, its performance remains unsatisfactory in many real-world applications, especially those where the…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
Cooperative optimization is a new way for finding global optima of complicated functions of many variables. It has some important properties not possessed by any conventional optimization methods. It has been successfully applied in solving…
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…
Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…
Ensembling methods are well known for improving prediction accuracy. However, they are limited in the sense that they cannot discriminate among component models effectively. In this paper, we propose stacking with auxiliary features that…
Probabilistic model checking computes probabilities and expected values related to designated behaviours of interest in Markov models. As a formal verification approach, it is applied to critical systems; thus we trust that probabilistic…
Modern data science relies on data analytic pipelines to organize interdependent computational steps. Such analytic pipelines often involve different algorithms across multiple steps, each with its own hyperparameters. To achieve the best…
Search and inference are two main strategies for optimally solving Distributed Constraint Optimization Problems (DCOPs). Recently, several algorithms were proposed to combine their advantages. Unfortunately, such algorithms only use an…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
This paper presents a novel optimization for differentiable programming named coarsening optimization. It offers a systematic way to synergize symbolic differentiation and algorithmic differentiation (AD). Through it, the granularity of the…
Operator overloading algorithmic differentiation (AD) tools are usually only developed for floating-point values. Algorithmic optimization for, e.g., linear systems solvers or matrix-matrix multiplications are often introduced via external…
We consider checkpointing strategies that minimize the number of recomputations needed when performing discrete adjoint computations using multistage time-stepping schemes, which requires computing several substeps within one complete time…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…