Related papers: On auxiliary latitudes
We present general algorithms to convert scattering data of linear and area detectors recorded in various scattering geometries to reciprocal space coordinates. The presented algorithms work for any goniometer configuration including…
In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…
In \cite{liu2022practical}, a general algorithm is developed to efficiently obtain the best accuracy using the regular refinement. The adaptive refinement allows for obtaining an accuracy with a smaller number of DoFs compared with the…
Modern lunar-planetary ephemerides are numerically integrated on the observational timespan of more than 100 years (with the last 20 years having very precise astrometrical data). On such long timespans, not only finite difference…
Accurate distance estimation from monocular cameras is essential for intelligent monitoring systems. In many deployments, image coordinates are mapped to ground positions using planar homographies initialized by manual selection of…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
Attitude estimation is the process of computing the orientation angles of an object with respect to a fixed frame of reference. Gyroscope, accelerometer, and magnetometer are some of the fundamental sensors used in attitude estimation. The…
We introduce and explain key relations between a posteriori error estimates and subspace correction methods viewed as preconditioners for problems in infinite dimensional Hilbert spaces. We set the stage using the Finite Element Exterior…
State machine formalisms equipped with hierarchy and parallelism allow to compactly model complex system behaviours. Such models can then be transformed into executable code or inputs for model-based testing and verification techniques.…
Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we prove a…
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of…
Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement…
The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated…
We study the multiple-precision addition of two positive floating-point numbers in base 2, with exact rounding, as specified in the MPFR library, i.e. where each number has its own precision. We show how the best possible complexity (up to…
A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…
We present fast and accurate ways to normalize two and three dimensional vectors and quaternions and compute their length. Our approach is an adaptation of ideas used in the linear algebra library LAPACK, and we believe that the…
In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and…
Transmission matrices, mapping the propagation of light from one end of the tissue to the other, form an important mathematical tool in the analysis of tissue scattering and the design of wavefront shaping systems. To understand the…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
This paper presents three novel algorithms for calculating geodesic intersections on an ellipsoid. These algorithms are applied in a case study analyzing real-time transit data in California to assess vehicle position drift. The analysis…