Finding the rotational matrix that minimizes the sum of squared deviations between two vectors is an important problem in bioinformatics and crystallography. Traditional algorithms involve the inversion or decomposition of a 3 x 3 or 4 x 4 matrix, which can be computationally expensive and numerically unstable in certain cases. Here, we present a simple and robust algorithm to rapidly determine...

We estimate the initial conditions of a multivariable dynamical system from a scalar signal, using a modified Newton-Raphson method incorporating the time evolution. We can estimate initial conditions of periodic and chaotic systems and the required length of scalar signal is very small. We also find that the information flow from one variable to the other has logarithmic dependence on time. An...

The stationary points of the potential energy function of the φ⁴ model on a two-dimensional square lattice with nearest-neighbor interactions are studied by means of two numerical methods: a numerical homotopy continuation method and a globally convergent Newton-Raphson method. We analyze the properties of the stationary points, in particular with respect to a number of quantities that have bee...

This paper presents an accurate and efficient method to solve both point projection and point inversion for NURBS curves and surfaces. We first subdivide the NURBS curve or surface into a set of Bézier subcurves or patches. Based on the relationship between the test point and the control polygon of Bézier curve or the control point net of the Bézier patch, we extract candidate Bézier subcurves ...

This paper illustrates two algorithms designed in Forneron and Ng (2020): the resampled Newton-Raphson (rNR) quasi-Newton (rQN) algorithms, which speed up estimation bootstrap inference for structural models. An empirical application to BLP shows that computation time decreases from nearly five hours with standard just over one hour rNR only 15 minutes using rQN. A first Monte Carlo exercise ac...

using the highly recommended numerical techniques, a finite element computer code is developed to analyse the steady incompressible, laminar and turbulent flows in 2-d domains with complex geometry. the petrov-galerkin finite element formulation is adopted to avoid numerical oscillations. turbulence is modeled using the two equation k-ω model. the discretized equations are written in the form o...

An e cient way of obtaining travelling waves in a periodic uid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a rst-order pseudospectral semi-implicit time scheme adapted to carry out the Newton’s iterations. The method is compared to a standard Newton–Raphson solver and is shown to be highly e cient in performing thi...

This paper presents a detailed description of the computer implementation of a generalized midpoint algorithm for integration of constitutive relations for von Mises’ hardening material. A nonlinear scalar equation for determination of the plastic multiplier is derived. The solution of this equation for a hardening material, by the Newton-Raphson method, usually converges in threefour iteration...

In this paper we present an algorithm for maximum likelihood estimation in the proportional odds model. The algorithm is an example of optimization transfer, also known as the method of iterative majorization. We discuss optimization transfer, present the proportional odds algorithm, and give a means for accelerating the convergence of the algorithm. The algorithm is stable and guaranteed to co...

| The use of the modiied Newton method for the solution of nonlinear magnetostatic problems arising from the vector potential Finite Element analysis is investigated. In particular the optimum choice of the relaxation factor is investigated. A new method is developed for determining the relaxation factor which minimizes the energy functional in the direction along the solution update at each no...