Related papers: A numerical algorithm for computing the zeros of p…
Given a large square matrix $A$ and a sufficiently regular function $f$ so that $f(A)$ is well defined, we are interested in the approximation of the leading singular values and corresponding singular vectors of $f(A)$, and in particular of…
Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
We estimate simple combination of the parabolic cylinder functions and their derivatives. These estimates are important for the spectral analysis of non-analytically perturbed quantum harmonic oscillator. The estimates are valid in rather…
The $\texttt{IntegerHull}$ function is part of Maple's $\texttt{PolyhedralSets}$ library, which calculates the integer hull of a given polyhedral set. This algorithm works by translating the supporting hyperplanes of the facets of the input…
We prove an Euler-Maclaurin formula for double polygonal sums and, as a corollary, we obtain approximate quadrature formulas for integrals of smooth functions over polygons with integer vertices. Our Euler-Maclaurin formula is in the spirit…
An approximate formula for complex Riemann Xi function, previously developed, is used to refine Backlund's estimate of the number of zeros till a chosen imaginary coordinate
We study the distribution of zeros of general solutions of the Airy and Bessel equations in the complex plane. Our results characterize the patterns followed by the zeros for any solution, in such a way that if one zero is known it is…
We present an algorithm for detecting basepoints of linear series of curves in the plane. Moreover, we give an algorithm for constructing a linear series of curves in the plane for given basepoints. The underlying method of these algorithms…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
We establish a new type of local asymptotic formula for the Green's function ${\mathcal G}_t(x,y)$ of a uniformly parabolic linear operator $\partial_t - L$ with non-constant coefficients using dilations and Taylor expansions at a point…
As we have shown several years ago [Y2], zeros of $L(s, \Delta )$ and $L^(2)(s, \Delta )$ can be calculated quite efficiently by a certain experimental method. Here $\Delta$ denotes the cusp form of weight 12 with respect to SL$(2, Z)$ and…
For nonsupersymmetric theories, the one-loop effective action can be computed via zeta function regularization in terms of the functional trace of the heat kernel associated with the operator which appears in the quadratic part of the…
We study the following ultraparabolic equation \[ \frac{\partial}{\partial t}u\left(t,s\right)+\frac{\partial}{\partial…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…
This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in arXiv:1304.0708 to global function fields of odd characteristics. First, we present algorithm for checking if a given…
Given a polynomial system f associated with a simple multiple zero x of multiplicity {\mu}, we give a computable lower bound on the minimal distance between the simple multiple zero x and other zeros of f. If x is only given with limited…
Various approaches to the numerical representation of the Incomplete Gamma Function F_m(z) for complex arguments z and small integer indexes m are compared with respect to numerical fitness (accuracy and speed). We consider power series,…
The fundamental solution (Green's function) of a first order matrix ordinary differential equation arising in a Landau-type problem is calculated by two methods. The coincidence of the two representations results in the integral formula for…
The article demonstrates the procedure how to compute the Zariski closure of an orbit by an algebraic action of finitely generated group on the affine plane. First half of the algorithm is about deciding whether given finitely generated…