Related papers: A Bivariate Preprocessing Paradigm for Buchberger-…
We present an accelerated, or 'look-ahead' version of the Newton-Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current…
The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…
In practice, deep neural networks are often able to easily interpolate their training data. To understand this phenomenon, many works have aimed to quantify the memorization capacity of a neural network architecture: the largest number of…
A new technique is presented to solve a class of linear boundary value problems (BVP). Technique is primarily based on an operational matrix developed from a set of modified Bernoulli polynomials. The new set of polynomials is an…
We consider the classical problems of interpolating a polynomial given a black box for evaluation, and of multiplying two polynomials, in the setting where the bit-lengths of the coefficients may vary widely, so-called unbalanced…
It was recently demonstrated that the boundary element method based on the Burton-Miller formulation (BM-BEM), widely used for solving exterior problems, can be adapted to solve transmission problems efficiently. This approach utilises…
This paper considers fast algorithms for operations on linearized polynomials. We propose a new multiplication algorithm for skew polynomials (a generalization of linearized polynomials) which has sub-quadratic complexity in the polynomial…
We present a FFT-based algorithm for the computation of a polynomial's coefficients from its roots, and apply it to obtain the coefficients of interpolation polynomials, to invert Vandermondians and to evaluate the symmetric functions of a…
We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and…
We use an interpolative technique from \cite{abps} to introduce the notion of multiple $N$-separately summing operators. Our approach extends and unifies some recent results; for instance we recover the best known estimates of the…
In this work, we introduce the Kaiser-Bessel interpolation basis for the particle-mesh interpolation in the fast Ewald method. A reliable a priori error estimate is developed to measure the accuracy of the force computation in correlated…
We propose a new more efficient method for the computation of two-sided Gr\"obner bases of ideals and bimodules shifting the problem to the enveloping algebra. Arising from the ideas this method involves, we introduce the notion of…
The paper gives an extension of Prony's method to the multivariate case which is based on the relationship between polynomial interpolation, normal forms modulo ideals and H--bases.
We present new techniques for reducing a multivariate sparse polynomial to a univariate polynomial. The reduction works similarly to the classical and widely-used Kronecker substitution, except that we choose the degrees randomly based on…
Lattice-based cryptographic algorithms built on ring learning with error theory are gaining importance due to their potential for providing post-quantum security. However, these algorithms involve complex polynomial operations, such as…
In this article we present a parallel modular algorithm to compute all solutions with multiplicities of a given zero-dimensional polynomial system of equations over the rationals. In fact, we compute a triangular decomposition using…
Developed by Buchberger for commutative polynomial rings, Groebner Bases are frequently applied to solve algorithmic problems, such as the congruence problem for ideals. Until now, these ideas have been transmitted to different in part…
A new efficient algorithm is proposed for factoring polynomials over an algebraic extension field. The extension field is defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its Groebner basis, no extra…
In contrast to the univariate case, interpolation with polynomials of a given maximal total degree is not always possible even if the number of interpolation points and the space dimension coincide. Due to that, numerous constructions for…
The aim of this paper is to study the approximation of functions using a higher order Hermite-Fejer interpolation process on the unit circle. The system of nodes is composed of vertically projected zeros of Jacobi polynomials onto the unit…