Related papers: Higher-Order Root-Finding Algorithm and its Applic…
In this paper we present an algorithm to obtain the parameter planes of families of root-finding methods with several free critical points. The parameter planes show the joint behaviour of all critical points. This algorithm avoids the…
Among many existing algorithms, convergence methods are the most popular means of computing square root and the reciprocal of square root of numbers. An initial approximation is required in these methods. Look up tables (LUT) are employed…
Levin Tree Search (LTS) (Orseau et al., 2018) is a search algorithm for deterministic environments that uses a user-specified policy to guide the search. It comes with a formal guarantee on the number of search steps (node visits) for…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
In this paper, we modify the Newton-Secant method with third order of convergence for finding multiple roots of nonlinear equations. Per iteration this method requires two evaluations of the function and one evaluation of its first…
Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…
Root-finders based on full linear multistep methods (LMMs) use previous function values, derivatives and root estimates to iteratively find a root of a nonlinear function. As ODE solvers, full LMMs are typically not zero-stable. However,…
Federated causal discovery aims to uncover the causal relationships between entities while protecting data privacy, which has significant importance and numerous applications in real-world scenarios. Existing federated causal structure…
The algorithms of Pan (1995) and(2002) approximate the roots of a complex univariate polynomial in nearly optimal arithmetic and Boolean time but require precision of computing that exceeds the degree of the polynomial. This causes…
Join ordering is the NP-hard problem of selecting the most efficient order in which to evaluate joins (conjunctive, binary operators) in a database query. Because query execution performance critically depends on this choice, join ordering…
Nearest neighbor search is a very active field in machine learning for it appears in many application cases, including classification and object retrieval. In its canonical version, the complexity of the search is linear with both the…
First order shape optimization methods, in general, require a large number of iterations until they reach a locally optimal design. While higher order methods can significantly reduce the number of iterations, they exhibit only local…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
A higher-order numerical method is presented for scalar valued, coupled forward-backward stochastic differential equations. Unlike most classical references, the forward component is not only discretized by an Euler-Maruyama approximation…
We describe a new method to accelerate neighbor searches on GRAPE, i.e. a special purpose hardware that efficiently calculates gravitational forces and potentials in $N$-body simulations. In addition to the gravitational calculations, GRAPE…
Path finding algorithm addresses problem of finding shortest path from source to destination avoiding obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike most path finding algorithms…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
High-resolution cameras have become very helpful for plant phenotyping by providing a mechanism for tasks such as target versus background discrimination, and the measurement and analysis of fine-above-ground plant attributes. However, the…
Finding relevant prior art is crucial when deciding whether to file a new patent application or invalidate an existing patent. However, searching for prior art is challenging due to the large number of patent documents and the need for…
In this paper we study the problem of finding the approximate nearest neighbor of a query point in the high dimensional space, focusing on the Euclidean space. The earlier approaches use locality-preserving hash functions (that tend to map…