Related papers: Algorithm 916: computing the Faddeyeva and Voigt f…
We propose a new practical algorithm for computing the Feigenbaum constants {\alpha} and {\delta}, having significantly lower time and space complexity than previously used methods. The algorithm builds upon well-known linear algebra…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
We present a new open source implementation in the SageMath computer algebra system of algorithms for the numerical solution of linear ODEs with polynomial coefficients. Our code supports regular singular connection problems and provides…
The paper concerns numerical algorithms for solving the Beltrami equation $f_{\bar{z}}(z)=\mu(z) f_z(z)$ for a compactly supported $\mu$. First, we study an efficient algorithm that has been proposed in the literature, and present its…
We present an efficient self-contained algorithm for computing the modified Bessel function of the first kind $I_{\nu}(z)$, implemented in a robust Fortran code supporting double and quadruple (quad) precision. The algorithm overcomes the…
Evaluating real-valued expressions to high precision is a key building block in computational mathematics, physics, and numerics. A typical implementation evaluates the whole expression in a uniform precision, doubling that precision until…
Evaluating real-valued expressions to high precision is a key building block in computational mathematics, physics, and numerics. A typical implementation evaluates the whole expression in a uniform precision, doubling that precision until…
In this work we develop a new algorithm for the efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where the number of the interpolation grid-points is dependent on the…
Weighted model counting computes the sum of the rational-valued weights associated with the satisfying assignments for a Boolean formula, where the weight of an assignment is given by the product of the weights assigned to the positive and…
Estimation of linear functionals from observed data is an important task in many subjects. Juditsky & Nemirovski [The Annals of Statistics 37.5A (2009): 2278-2300] propose a framework for non-parametric estimation of linear functionals in a…
Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given…
The Cadzow's algorithm is a signal denoising and recovery method which was designed for signals corresponding to low rank Hankel matrices. In this paper we first introduce a Fast Cadzow's algorithm which is developed by incorporating a…
We discuss the best methods available for computing the gamma function $\Gamma(z)$ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small…
We prove simple general formulas for expectations of functions of a random walk and its running extremum. Under additional conditions, we derive analytical formulas using the inverse $Z$-transform, the Fourier/Laplace inversion and…
For accurate line-by-line modeling of molecular cross sections several physical processes "beyond Voigt" have to be considered. For the speed-dependent Voigt and Rautian profiles (SDV, SDR) and the Hartmann-Tran profile the difference $w(i…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
The paper presents (human-oriented) specification and (pen-and-paper) verification of the square root function. The function implements Newton method and uses a look-up table for initial approximations. Specification is done in terms of…
The purpose of this article is to propose ODE based approaches for the numerical evaluation of matrix functions $f(A)$, a question of major interest in the numerical linear algebra. To this end, we model $f(A)$ as the solution at a finite…
Solutions to a wide variety of transcendental equations can be expressed in terms of the Lambert $\mathrm{W}$ function. The $\mathrm{W}$ function, occurring frequently in applications, is a non-elementary, but now standard mathematical…
We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function,…