Related papers: Approximation of Multiple Integrals over Hyperbolo…
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…
We investigate the approximation of weighted integrals over $\mathbb{R}^d$ for integrands from weighted Sobolev spaces of mixed smoothness. We prove upper and lower bounds of the convergence rate of optimal quadratures with respect to $n$…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
We consider polynomials of a few linear forms and show how exploit this type of sparsity for optimization on some particular domains like the Euclidean sphere or a polytope. Moreover, a simple procedure allows to detect this form of…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
Efficiently pricing multi-asset options poses a significant challenge in quantitative finance. Fourier methods leverage the regularity properties of the integrand in the Fourier domain to accurately and rapidly value options that typically…
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
Practically relevant problems of quadratic optimization often contain multidimensional arrays of variables interconnected by linear constraints, such as equalities and inequalities. The values of each variable depend on its specific meaning…
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…
We study the bias-variance tradeoff within a multiscale approximation framework. Our approach uses a given quasi-interpolation operator, which is repeatedly applied within an error-correction scheme over a hierarchical data structure. We…
Quantization algorithms have been successfully adopted to option pricing in finance thanks to the high convergence rate of the numerical approximation. In particular, very recently, recursive marginal quantization has been proven to be a…
We consider digitized-counterdiabatic quantum computing as an advanced paradigm to approach quantum advantage for industrial applications in the NISQ era. We apply this concept to investigate a discrete mean-variance portfolio optimization…
In this paper, a transform approach is used for polycyclic and serial codes over finite local rings in the case that the defining polynomials have no multiple roots. This allows us to study them in terms of linear algebra and invariant…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
We present and discuss different algorithms for converting rectangular imagery into elliptical regions. We mainly focus on methods that use mathematical mappings with explicit and invertible equations. The key idea is to start with…
Based on the characterization of the polyconvex envelope of isotropic functions by their signed singular value representations, we propose a simple algorithm for the numerical approximation of the polyconvex envelope. Instead of operating…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…