Related papers: New Approximation method for the computation of pa…
A simple algorithm with quasi-linear time complexity and linear space complexity for the evaluation of the hypergeometric series with rational coefficients is constructed. It is shown that this algorithm is suitable in practical informatics…
This paper describes a practical methodology for computing the Hardy function Z(t), using just O(((t/epsilon)^(1/3))*(log(t))^(2+o(1)))) standard computational operations, to a tolerance of epsilon in the relative error. The methodology is…
Let $L$ be a set of $n$ lines in the plane. The zone $Z(\ell)$ of a line $\ell$ in the arrangement $\mathcal{A}(L)$ of $L$ is the set of faces of $\mathcal{A}(L)$ whose closure intersects $\ell$. It is known that the combinatorial size of…
$\renewcommand{\Re}{\mathbb{R}}\newcommand{\eps}{{\varepsilon}}\newcommand{\poly}{\mathrm{poly}} $In this paper, we study the problem of $L_1$-fitting a shape to a set of $n$ points in $\Re^d$ (where $d$ is a fixed constant), where the…
We present an algorithm which, given a linear recurrence operator $L$ with polynomial coefficients, $m \in \mathbb{N}\setminus\{0\}$, $a_1,a_2,\ldots,a_m \in \mathbb{N}\setminus\{0\}$ and $b_1,b_2,\ldots,b_m \in \mathbb{K}$, returns a…
In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.
We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string.…
In this paper we present a new family of identities for Euler sums and integrals of polylogarithms by using the methods of generating function and integral representations of series. Then we apply it to obtain the closed forms of all…
Numerical data processing is a key task across different fields of computer technology use. However, even simple summation of values is not precise due to the floating point representation use. This paper presents a practical algorithm for…
We derive a compact determinant formula for calculating and factorizing the hypersum polynomials S^{(L)}_k(N) \equiv \sum_{n_1=1}^N ...\sum_{n_{L+1}=1}^{n_{L}}(n_{L+1})^k expressed in the variable N(N+L+1)
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…
We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires…
A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…
Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…
It is widely known that the lower bound for the algorithmic complexity of square matrix multiplication resorts to at least $n^2$ arithmetic operations. The justification builds upon the following reasoning: given that there are $2 n^2$…
We draw attention to simplifications in the theory of a N\"orlund summation method $(N, p)$ that arise when the series $\sum_{n \geqslant 0} p_n$ is convergent.
The Unbounded Subset-Sum Problem (USSP) is defined as: given sum $s$ and a set of integers $W\leftarrow \{p_1,\dots,p_n\}$ output a set of non-negative integers $\{y_1,\dots,y_n\}$ such that $p_1y_1+\dots+p_ny_n=s$. The USSP is an…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
Let $\cp:=(P_1,...,P_s)$ be a given family of $n$-variate polynomials with integer coefficients and suppose that the degrees and logarithmic heights of these polynomials are bounded by $d$ and $h$, respectively. Suppose furthermore that for…
Approximative properties of linear summation methods of Fourier series are considered in the Orlicz type spaces ${\mathcal S}_{M}$. In particular, in terms of approximations by such methods, constructive characteristics are obtained for…