相关论文: Volume computation for polytopes and partition fun…
In this article, we discuss how a kind of hybrid computation, which employs symbolic, numeric, classic, and quantum algorithms, allows us to conduct Hartree-Fock electronic structure computation of molecules. In the proposed algorithm, we…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and…
On the basis of the generalized argument principle, here we develop a numerical scheme for locating zeros and poles of a meromorphic function. A subdivision-transformation-calculation scheme is proposed to ensure the algorithm stability. A…
We give a combinatorial interpretation for the hypergeometric functions associated with tuples of rational numbers.
The harmonic chain is a classical many-particle system which can be solved exactly for arbitrary number of particles (at least in simple cases, such as equal masses and spring constants). A nice feature of the harmonic chain is that the…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
We devise a simple but remarkably accurate iterative routine for calculating the roots of a polynomial of any degree. We demonstrate that our results have significant improvement in accuracy over those obtained by methods used in popular…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
A vector partition function is the number of ways to write a vector as a non-negative integer-coefficient sum of the elements of a finite set of vectors $\Delta$. We present a new algorithm for computing closed-form formulas for vector…
We compute the intrinsic volumes of the cone of positive semidefinite matrices over the real numbers, over the complex numbers, and over the quaternions, in terms of integrals related to Mehta's integral. Several applications for the…
We develop a parallel algorithm that calculates the exact partition function of a lattice polymer, by enumerating the number of conformations for each energy level. An efficient parallelization of the calculation is achieved by classifying…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…
The volume is an important attribute of a convex body. In general, it is quite difficult to calculate the exact volume. But in many cases, it suffices to have an approximate value. Volume estimation methods for convex bodies have been…
We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure…
In contrast to an infinite family of explicit examples of two-dimensional $p$-harmonic functions obtained by G.Aronsson in the late 80s, there is very little known about the higher-dimensional case. In this paper, we show how to use…
The functional determinant of Laplace-type operators on the 3-dimensional non-compact hyperbolic manifold with invariant fundamental domain of finite volume is computed by quadratures and making use of the related terms of the Selberg trace…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
We introduce a method and an algorithm for computing the weighted Moore-Penrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices. These methods and algorithms are…