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Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
For a linearly recurrent vector sequence P[n+1] = A(n) * P[n], consider the problem of calculating either the n-th term P[n] or L<=n arbitrary terms P[n_1],...,P[n_L], both for the case of constant coefficients A(n)=A and for a matrix A(n)…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
We describe a provably quasi-polynomial algorithm to compute discrete logarithms in the multiplicative groups of finite fields of small characteristic, that is finite fields whose characteristic is logarithmic in the order. We partially…
Evaluation of the Voigt function, a convolution of a Lorentzian and a Gaussian profile, is essential in various fields such as spectroscopy, atmospheric science, and astrophysics. Efficient computation of the function is crucial, especially…
Some integral properties of Jack polynomials, hypergeometric functions and invariant polynomials are studied for real normed division algebras.
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
We investigate deep composite polynomial approximations of continuous but non-differentiable functions with algebraic cusp singularities. The functions in focus consist of finitely many cusp terms of the form $|x-a_j|^{\alpha_j}$ with…
We consider the problem of finding the set of classical polylogarithmic functions $\text{Li}_n$ with branching locus determined by the solution of $p_1\cdot p_2\cdot \ldots \cdot p_n=0$, where $p_1,\ldots, p_n$ are irreducible polynomials…
We use the theory of motivic integration in order to give a geometric explanation of the behavior of some p-adic integrals.
This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for $H(\rm curl)$, $H(\rm div)$ and $H(\rm divdiv)$ problems, based on $H^1$ auxiliary space decomposition. The proposed framework employs…
The logarithmic potential is of great interest and relevance in the study of the dynamics of galaxies. Some small corrections to the work of Contopoulos & Seimenis (1990) who used the method of Prendergast (1982) to find periodic orbits and…
In this paper we present efficient computational and symbolic algorithms for solving a nearly pentadiagonal linear systems. The implementation of the algorithms using Computer Algebra Systems (CAS)such as MAPLE, MACSYMA, MATHEMATICA, and…
A convolution approach leading to an explicit computation of a value of a 4F3 function is outlined. We also investigate about the role of the dilogarithm reflection formula, leading to a remarkable consequence: in some cases, values of 4F3…
We show that Hermite's approximations to values of the exponential function at given algebraic numbers are nearly optimal when considered from an adelic perspective. We achieve this by taking into account the ratio of these values whenever…
In this article, we study pseudo-differential equations involving semi-quasielliptic symbols over p-adics. We determine the function spaces where such equations have solutions. We introduce the space of infinitely pseudo-differentiable…
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…