Related papers: Deriving Sorting Algorithms
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
New families of composition methods with processing of order 4 and 6 are presented and analyzed. They are specifically designed to be used for the numerical integration of differential equations whose vector field is separated into three or…
Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random…
In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…
Much of the copious literature on the subject of sorting has concentrated on minimizing the number of comparisons and/or exchanges/copies. However, a more appropriate yardstick for the performance of sorting algorithms is based on the total…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
The dynamic partial sorting problem asks for an algorithm that maintains lists of numbers under the link, cut and change value operations, and queries the sorted sequence of the $k$ least numbers in one of the lists. We first solve the…
We present an efficient and robust reference resolution algorithm in an end-to-end state-of-the-art information extraction system, which must work with a considerably impoverished syntactic analysis of the input sentences. Considering this…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
In this work, we argue for the importance of causal reasoning in creating fair algorithms for decision making. We give a review of existing approaches to fairness, describe work in causality necessary for the understanding of causal…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
There is a growing concern about typically opaque decision-making with high-performance machine learning algorithms. Providing an explanation of the reasoning process in domain-specific terms can be crucial for adoption in risk-sensitive…
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…
In this paper we present an alternative approach to symbolic segmentation; instead of implementing a new method we approach symbolic segmentation as an algorithm selection problem. That is, let there be $n$ available algorithms for symbolic…
We introduce a sorting machine consisting of $k+1$ stacks in series: the first $k$ stacks can only contain elements in decreasing order from top to bottom, while the last one has the opposite restriction. This device generalizes \cite{SM},…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more…
The sorting operation is one of the most commonly used building blocks in computer programming. In machine learning, it is often used for robust statistics. However, seen as a function, it is piecewise linear and as a result includes many…