Related papers: Constructing Polynomial Block Methods
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
In this paper we present algorithms for collective construction systems in which a large number of autonomous mobile robots trans- port modular building elements to construct a desired structure. We focus on building block structures…
This article extends the theory of classical finite-difference summation-by-parts (FD-SBP) time-marching methods to the generalized summation-by-parts (GSBP) framework. Dual-consistent GSBP time-marching methods are shown to retain: A and…
When one wishes to numerically solve an initial value problem, it is customary to rewrite it as an equivalent first-order system to which a method, usually from the class of Runge-Kutta methods, is applied. Directly treating higher-order…
A wide range of physical phenomena exhibit auxiliary admissibility criteria, such as conservation of entropy or various energies, which arise implicitly under exact solution of their governing PDEs. However, standard temporal schemes, such…
High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…
In this paper we give a new aggregation framework for linear Diophantine equations. In particular, we prove that an aggregated system of minimum size can be built in polynomial time. We also derive an analytic formula that gives the number…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
There are several efficient methods to solve linear interval polynomial systems in the context of interval computations, however, the general case of interval polynomial systems is not yet covered as well. In this paper we introduce a new…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…
Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In recent works of the authors the…
Different possible sources are discussed for enhancement of the calculation time when solving ordinary differential equations systems to forecast space objects' motion. This paper presents an approach for building an integrator of ordinary…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
This paper extends a polynomial-time parsing algorithm that resolves structural ambiguity in input to a speech-based user interface by calculating and comparing the denotations of rival constituents, given some model of the interfaced…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
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…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
In this work, we investigate a model order reduction scheme for polynomial parametric systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order…
This paper investigates numerical methods for solving coupled system of nonlinear elliptic problems. We utilize block monotone iterative methods based on Jacobi and Gauss--Seidel methods to solve difference schemes which approximate the…