In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...

Much recent attention has been devoted to gradient descent algorithms where the steepest descent step size is replaced by a similar one from a previous iteration or gets updated only once every second step, thus forming a faster gradient descent method. For unconstrained convex quadratic optimization these methods can converge much faster than steepest descent. But the context of interest here ...

The purpose of this study is to analyze the performance of Back propagation algorithm with changing training patterns and the second momentum term in feed forward neural networks. This analysis is conducted on 250 different words of three small letters from the English alphabet. These words are presented to two vertical segmentation programs which are designed in MATLAB and based on portions (1...

BACKGROUND Studies have shown a clear relationship between depressive disorders and vitamin B12 deficiency. Gastroenteritis and Helicobacter pylori infections can cause vitamin B12 deficiency. Helicobacter pylori infections are not uncommon among people of Turkish descent in The Netherlands. AIM To examine the frequency of vitamin B12 deficiency in depressive patients of Turkish descent and c...

We study a class of minisuperspace models consisting of a homogeneous isotropic universe with a minimally coupled homogeneous scalar field with a potential ct cosh{2')+P sinh{2$), where a and P are arbitrary parameters. This includes the case of a pure exponential potential exp{2$), which arises in the dimensional reduction to four dimensions of five-dimensional Kaluza-Klein theory. We study th...

In this thesis I will describe an explicit method for performing an 8-descent on elliptic curves. First I will present some basics on descent, in particular I will give a generalization of the definition of n-coverings, which suits the needs of higher descent. Then I will sketch the classical method of 2-descent, and the two methods that are known for doing a second 2-descent, also called 4-des...

Let L/K be a field extension. A K-vector space W can be extended to an L-vector space L⊗KW , and W embeds into L⊗KW by w 7→ 1⊗w. Under this embedding, when W 6= 0 a K-basis {ei} of W turns into an L-basis {1⊗ ei} of L⊗KW . Passing from W to L⊗KW is called ascent. In the other direction, if we are given an L-vector space V 6= 0, we may ask how to describe the K-subspaces W ⊂ V such that a K-basi...

This paper studies the regret of a family of distributed algorithms for online convex unconstrained optimization. A team of agents cooperate in a decision making process enabled by local interactions and the knowledge of each agent about the local cost functions associated with its decisions in previous rounds. We propose a class of online, second-order distributed coordination algorithms that ...

In this paper we derive uniform asymptotic expansions for the partial sums of the exponential series. We indicate how this information will be used in a later publication to obtain full and explicitly computable asymptotic expansions with error bounds for all zeros of the Taylor polynomials pn−1(z) = Pn−1 k=0 z/ k! . Our proof is based on a representation of pn−1(nz) in terms of an integral of ...