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We study computational methods for the approximation of special functions recurrent in geometric function theory and quasiconformal mapping theory. The functions studied can be expressed as quotients of complete elliptic integrals and as…
Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were…
In this note we deal with some inequalities for the tangent function that are valid for $x$ in $(-\pi/2,\pi/2)$. These inequalities are optimal in the sense that the best values of the exponents involved are obtained.
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…
A major challenge for matching-based depth estimation is to prevent mismatches in occlusion and smooth regions. An effective matching window satisfying three characteristics: texture richness, disparity consistency and anti-occlusion should…
Illuminating or imaging samples from a broad angular range is essential in a wide variety of computational 3D imaging and resolution-enhancement techniques, such as optical projection tomography (OPT), optical diffraction tomography (ODT),…
We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
A novel technique for calibration transfer called the Modified Four Point Interpolant (MFPI) method is introduced for near infrared spectra. The method is founded on physical intuition and utilizes a series of quasiconformal maps in the…
We present an analytic approximation model for non-rigid point set registration, grounded in the multivariate Taylor expansion of vector-valued functions. By exploiting the algebraic structure of Taylor expansions, we construct a structured…
The complete $p$-elliptic integrals are generalizations of the complete elliptic integrals by the generalized trigonometric function $\sin_p{\theta}$ and its half-period $\pi_p$. It is shown, only for $p=4$, that the generalized…
This study presents an analytical method for tuning PI controllers in First-Order with Time Delay (FOTD) systems, leveraging the Lambert W function. The Lambert W function enables exact pole placement, yielding analytical expressions for PI…
The exact estimation of latent variable models with big data is known to be challenging. The latents have to be integrated out numerically, and the dimension of the latent variables increases with the sample size. This paper develops a…
We propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our…
We present an efficient algorithm designed for and capable of detecting elongated, thin features such as lines and curves in astronomical images, and its application to the automatic detection of gravitational arcs. The algorithm is…
In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…
To infer a function value on a specific point $x$, it is essential to assign higher weights to the points closer to $x$, which is called local polynomial / multivariable regression. In many practical cases, a limited sample size may ruin…
In this paper, we develop and test a fast numerical algorithm, called MDI-LR, for efficient implementation of quasi-Monte Carlo lattice rules for computing $d$-dimensional integrals of a given function. It is based on the idea of converting…
Many of the fastest known algorithms to compute $\pi$ involve generalized hypergeometric series, such as the Ramanujan-Sato series. In this paper, we investigate the rates of convergence for several such series and we give asymptotic…
This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated and on its base a computationally effective algorithm is constructed for decomposition of a…