Most discussions of John Maynard Keynes's activities in connection with Newton are restricted to the sale in 1936 at Sotheby's of Newton's Portsmouth Papers and to Keynes's 1946 essay 'Newton, the Man'. This paper provides a history of Keynes's Newton-related work in the interim, highlighting especially the events of 1942 and 1943, which were particularly relevant to the Royal Society's role in...

We present the first adaptive random directions Newton algorithm under i.i.d., symmetric, uniformly distributed perturbations for a general problem of optimization under noisy observations. We also present a simple gradient search scheme under the aforementioned perturbation random variates. Our Newton algorithm requires generating N perturbation variates and three simulations at each iteration...

Newton corpuscular theory: According to Newton light energy propagates from one point to another in the form of particle. From the source of light very small tiny particles are emitted in all directions which travel with a tremendous speed 3 x 10 m/sec and when these corpuscles strike the retina of eye we feel the sensation of light. Newton attributed different colors to the different size of t...

The full-space Lagrange–Newton algorithm is one of the numerical algorithms for solving problems arising from optimization problems constrained by nonlinear partial differential equations. Newton-type methods enjoy fast convergence when the nonlinearity in the system is well-balanced; however, for some problems, such as the control of incompressible flows, even linear convergence is difficult t...

One of the widely used methods for solving a nonlinear system of equations is the quasi-Newton method. The basic idea underlining this type of method is to approximate the solution of Newton's equation by means of approximating the Jacobian matrix via quasi-Newton update. Application of quasi-Newton methods for large scale problems requires, in principle, vast computational resource to form and...

Newton iteration is known (under some precise conditions) to converge quadratically to zeros of non-degenerate systems of polynomials. This and other properties may be used to obtain theorems on the global complexity of solving systems of polynomial equations (See Shub and Smale in [6]), using a model of computability over the reals. However, it is not practical (and not desirable) to actually ...

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if it is hard to approximate the Hessian well and efficiently. As far as we know, there is no effective way to handle this problem. In this paper, we resort to N...

Introduction: The aim of this study was to evaluate the effect of proximal contour of class II composite restorations placed with straight or contoured matrix band using composite resins with different modulus of elasticity on stress distribution by finite element method. Methods: In order to evaluate the stress distribution of class II composite restorations using finite element method, upper ...