Related papers: ARPIST: Provably Accurate and Stable Numerical Int…
We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting…
We introduce a novel quantum computing heuristic for solving the irregular strip packing problem, a significant challenge in optimizing material usage across various industries. This problem involves arranging a set of irregular polygonal…
We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which…
In the classic circle packing problem, one asks whether a given set of circles can be packed into a given container. Packing problems like this have been shown to be $\mathsf{NP}$-hard. In this paper, we present new sufficient conditions…
In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…
We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces…
The stochastic three points (STP) algorithm is a derivative-free optimization technique designed for unconstrained optimization problems in $\mathbb{R}^d$. In this paper, we analyze this algorithm for three classes of functions: smooth…
We present a method for obtaining efficient probabilistic solutions to geostatistical and linear inverse problems in spherical geometry. Our Spherical Direct Sequential Simulation (SDSSIM) framework combines information from possibly noisy…
In this study, using the analytical and recurrence relations suggested by the authors in previous works, the new efficient and reliable program procedure for the overlap integrals over Slater type orbitals (STOs) is presented. The proposed…
We introduce Spiral, a third-order integration algorithm for the rotational motion of extended bodies. It requires only one force calculation per time step, does not require quaternion normalization at each time step, and can be formulated…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
Trust-region (TR) and adaptive regularization using cubics (ARC) have proven to have some very appealing theoretical properties for non-convex optimization by concurrently computing function value, gradient, and Hessian matrix to obtain the…
Increasing the angular resolution of an interferometric array requires placing its elements at large separations. This often leads to sparse coverage and introduces challenges to reconstructing images from interferometric data. We introduce…
Sphericity and roundness are fundamental measures used for assessing object uniformity in 2D and 3D images. However, using their strict definition makes computation costly. As both 2D and 3D microscopy imaging datasets grow larger, there is…
We describe our implementation of a global-parameter optimizer and Square Root Information Filter (SRIF) into the asteroid-modelling software SHAPE. We compare the performance of our new optimizer with that of the existing sequential…
In [1], the author considered the problem of the optimal approximation of symmetric surfaces by biquadratic B\'ezier patches. Unfortunately, the results therein are incorrect, which is shown in this paper by considering the optimal…
The aim of this paper is to present a new fast-convergent numerically stable space-time adaptive processing (STAP) algorithm derived using a novel technique of feedback orthogonalization. The main advantages of this approach lie in its…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…