Related papers: An algorithm for computing the integral closure
This paper introduces the theory and hardware implementation of two new algorithms for computing a single component of the discrete Fourier transform. In terms of multiplicative complexity, both algorithms are more efficient, in general,…
In this paper, we propose a numerical method of computing Hadamard finite-part integrals with an integral power singularity at the endpoint on a half infinite interval, that is, a finite value assigned to a divergent integral with an…
An integro-differential ring is a differential ring that is closed under an integration operation satisfying the fundamental theorem of calculus. Via the Newton--Leibniz formula, a generalized evaluation is defined in terms of integration…
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann…
Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If G_C-dimension of M/IM is finite for all ideals I generated by an R-regular sequence of length…
In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous…
The theory of border bases for zero-dimensional ideals has attracted several researchers in symbolic computation due to their numerical stability and mathematical elegance. As shown in (Francis & Dukkipati, J. Symb. Comp., 2014), one can…
A numerical scheme is presented to solve the one source near field refractor problem to arbitrary precision and it is proved that the scheme terminates in a finite number of iterations. The convergence of the algorithm depends upon proving…
A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is…
Low rank matrix approximation is a popular topic in machine learning. In this paper, we propose a new algorithm for this topic by minimizing the least-squares estimation over the Riemannian manifold of fixed-rank matrices. The algorithm is…
We classify certain resolving subcategories of finitely generated modules over a commutative noetherian ring R by using integer-valued functions on Spec R. As an application we give a complete classification of resolving subcategories when…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction $A + A \rightarrow\varnothing$ modeling is discussed. Finite difference method together with the linear…
We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.
This paper presents a conception for computing gr\"{o}bner basis. We convert some of gr\"{o}bner-computing algorithms, e.g., F5, extended F5 and GWV algorithms into a special type of algorithm. The new algorithm's finite termination problem…
A new expression for solving homogeneous linear ODEs based on a generalization of the Volterra composition was recently introduced. In this work, we extend such an expression, showing that it corresponds to inverting an infinite matrix.…
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…
Let $R$ be a (commutative Noetherian) local ring of prime characteristic that is $F$-pure. This paper studies a certain finite set ${\mathcal I}$ of radical ideals of $R$ that is naturally defined by the injective envelope of the simple…
In this paper we discuss two different existing algorithms for computing topological entropy and we perform one of them in order to compute the isentropes for cubic polynomials.