The Newtonian method is a standard iterative method with quadratic convergence rates for solving large optimization problems. The Support Vector Machine problem formulation requires the solution of large datasets, which is ideal for the application of Newtonian methods. We point out that the Sequential Minimal Optimization (SMO) algorithm is a Newtonian Decomposition Method that is popular due ...

Abstract The Boosted Difference of Convex functions Algorithm (BDCA) has been recently introduced to accelerate the performance classical (DCA). This acceleration is achieved thanks an extrapolation step from point computed by DCA via a line search procedure. In this work, we propose extension BDCA that can be applied difference convex programs with linear constraints, and prove every cluster s...

We develop a cosmological model based on a quadratic equation of state p/c = −(α + 1)ρ/ρP + αρ− (α + 1)ρΛ, where ρP is the Planck density and ρΛ the cosmological density, “unifying” vacuum energy and dark energy in the spirit of a generalized Chaplygin gas model. For ρ → ρP , it reduces to p = −ρP c leading to a phase of early accelerating expansion (early inflation) with a constant density equ...

In the present paper, we give approximate values of π deduced from the areas of inscribed and circumscribed quadratic and cubic circular splines. Similar results on circular splines of higher degrees and higher approximation orders can be obtained in the same way. We compare these values to those obtained by computing the perimeters of those circular splines. We observe that the former are much...

The relationship between quadratic mean diameter and tree density appeared curvilinear on a log-log scale, based on data from direct-seeded slash pine (Pinus elliottii var. elliottii Engelm.) stands. The self-thinning trajectory followed a straight line for high tree density levels and then turned away from this line as tree density decreased. A system of equations was developed to model the re...

We consider the inversion of a linear operator with centered Gaussian white noise by MAP estimation with a Gaussian prior distribution on the solution. The actual estimator is computed approximately by a numerical method. We propose a relation between the stationarity measure of this approximate solution to the mean square error of the exact solution. This relation enables the formulation of a ...

In this paper we study a binomial model with random time steps and explain how to calculate values for European and American call and put options. We prove both weak convergence of the discrete processes to the Black}Scholes setup and convergence of the values for European and American put options. Computational experiments exhibit a smooth convergence structure and suggest that we can obtain a...

We have evaluated radiosensitivity parameters for cellular transformation from published experimental data on neoplastic transformations induced in C3H10T1/2 cells by BEVALAC ions. The measured RBE values are well reproduced by a track theory calculation using sets of m-target parameters with either m = 2 or m = 3, suggesting a quadratic or cubic extrapolation to low doses of gamma rays. Using ...

Using a 25-y time series of precision satellite altimeter data from TOPEX/Poseidon, Jason-1, Jason-2, and Jason-3, we estimate the climate-change-driven acceleration of global mean sea level over the last 25 y to be 0.084 ± 0.025 mm/y2 Coupled with the average climate-change-driven rate of sea level rise over these same 25 y of 2.9 mm/y, simple extrapolation of the quadratic implies global mean...