Related papers: Improved Aberth-Ehrlich root-finding algorithm and…

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…

We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe…

We report the result of the analysis of the light curve of the microlensing event MOA-2009-BLG-016. The light curve is characterized by a short-duration anomaly near the peak and an overall asymmetry. We find that the peak anomaly is due to…

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a real coefficient polynomial. They can be approximated at a low computational cost if the…

I present a previously unpublished method for modeling multiple lens microlensing events that is based on the image centered ray shooting approach of Bennett and Rhie. It has been used to model all a wide variety of binary and triple lens…

We present the bilateral solver, a novel algorithm for edge-aware smoothing that combines the flexibility and speed of simple filtering approaches with the accuracy of domain-specific optimization algorithms. Our technique is capable of…

We analyze accretion-rate time series for equal-mass binaries in co-planar gaseous disks spanning a continuous range of orbital eccentricities up to 0.8, for both prograde and retrograde systems. The dominant variability timescales match…

The Durand-Kerner algorithm is a widely used iterative technique for simultaneously finding all the roots of a polynomial. However, its convergence heavily depends on the choice of initial approximations. This paper introduces two novel…

Microlensing can provide an important tool to study binaries, especially those composed of faint or dark objects. However, accurate analysis of binary-lens light curves is often hampered by the well-known degeneracy between close (s<1) and…

We present an accelerated, or 'look-ahead' version of the Newton-Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current…

A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…

We study the complexity of polynomial multiplication over arbitrary fields. We present a unified approach that generalizes all known asymptotically fastest algorithms for this problem. In particular, the well-known algorithm for…

Since the first microlensing planet discovery in 2003, more than 200 planets have been detected with gravitational microlensing, in addition to several free-floating planet and black hole candidates. In this chapter the microlensing theory…

We introduce novel polynomial deformations of the Lie algebra $sl(2)$. We construct their finite-dimensional irreducible representations and the corresponding differential operator realizations. We apply our results to a class of spin…

A minimal solution using two affine correspondences is presented to estimate the common focal length and the fundamental matrix between two semi-calibrated cameras - known intrinsic parameters except a common focal length. To the best of…

(abridged) Using the particularly long gravitational microlensing event OGLE-2014-BLG-1186 with a time-scale $t_\mathrm{E}$ ~ 300 d, we present a methodology for identifying the nature of localised deviations from single-lens point-source…

This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…

Once a gravitational wave signal is detected, the measurement of its source parameters is important to achieve various scientific goals. This is done through Bayesian inference, where the analysis cost increases with the model complexity…

We study the problem of local alignment, which is finding pairs of similar subsequences with gaps. The problem exists in biosequence databases. BLAST is a typical software for finding local alignment based on heuristic, but could miss…

This paper presents a comprehensive analysis of the well-known extragradient (EG) method for solving both equations and inclusions. First, we unify and generalize EG for [non]linear equations to a wider class of algorithms, encompassing…