Exercise sheet 3 pdf

Exercises and solutions in PDF

On The Critical Points of some Iteration Methods for Solving Algebraic Equations. Global Convergence Properties

In this work we give su±cient conditions for k-th approximations of the polynomial roots of f(x) when the Maehly{Aberth{Ehrlich, Werner-Borsch-Supan, Tanabe, Improved Borsch-Supan iteration methods fail on the next step. For these methods all non-attractive sets are found. This is a subsequent improvement of previously developed techniques and known facts. The users of these methods can use the results presented here for software implementation in Distributed Applications and Simulation Environ- ments. Numerical examples with graphics are shown.

On the Critical Points of Kyurkchiev’s Method for Solving Algebraic Equations

This paper is dedicated to Prof. Nikolay Kyurkchiev on the occasion of his 70th anniversary This paper gives sufficient conditions for kth approximations of the zeros of polynomial f (x) under which Kyurkchiev’s method fails on the next step. The research is linked with an attack on the global convergence hypothesis of this commonly used in practice method (as correlate hypothesis for Weierstrass–Dochev’s method). Graphical examples are presented.

On Arrangements of Real Roots of a Real Polynomial and Its Derivatives

2000 Mathematics Subject Classification: 12D10.

A method for solving polynomial equations by continued fractions.

Bibliography: p. 16.

On the Hyperbolicity Domain of the Polynomial x^n + a1x^(n-1) + 1/4+ an

∗ Partially supported by INTAS grant 97-1644

On the Factorization of the Poincaré Polynomial: A Survey

2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.

Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences

ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2.

Designing for participation in local social ridesharing networks : grass roots prototyping of IT systems

This abstract explores the possibility of a grass roots approach to engaging people in community change initiatives by designing simple interactive exploratory prototypes for use by communities over time that support shared action. The prototype is gradually evolved in response to community use, fragments of data gathered through the prototype, and participant feedback with the goal of building participation in community change initiatives. A case study of a system to support ridesharing is discussed. The approach is compared and contrasted to a traditional IT systems procurement approach.

Model-order selection in Zernike polynomial expansion of corneal surfaces using the efficient detection criterion

Corneal-height data are typically measured with videokeratoscopes and modeled using a set of orthogonal Zernike polynomials. We address the estimation of the number of Zernike polynomials, which is formalized as a model-order selection problem in linear regression. Classical information-theoretic criteria tend to overestimate the corneal surface due to the weakness of their penalty functions, while bootstrap-based techniques tend to underestimate the surface or require extensive processing. In this paper, we propose to use the efficient detection criterion (EDC), which has the same general form of information-theoretic-based criteria, as an alternative to estimating the optimal number of Zernike polynomials. We first show, via simulations, that the EDC outperforms a large number of information-theoretic criteria and resampling-based techniques. We then illustrate that using the EDC for real corneas results in models that are in closer agreement with clinical expectations and provides means for distinguishing normal corneal surfaces from astigmatic and keratoconic surfaces.

Retracing the Roots and Ideals of Confucian Principles of Governance: the Art of Regulating Governance without Legal Rules in Chinese Societies

Confucius was and still is one of the most eminent Chinese philosophers. Such is the importance of Confucius’s teachings; it had influenced all aspects of social life in Chinese societies. In the post-Enron, post-Worldcom, and post-Global Financial Crisis era there are raising doubts in the mantra of the so-called conventional wisdom about law and economic order. Whilst many recent publications offered solutions to those problems like advocating for more laws, rules or reforms in regulatory institutions to enhance the regulation of corporate governance. What Confucius advocated was a non-legal, social mode of regulation based on moral ideals that should be embedded into the minds of every person. Whilst this is an ancient concept from primitive societies, its relevance and merits could be seen in modern Chinese societies like Hong Kong. In essence, Confucian principles of governance build on relational and paternalistic order based on moral ideals.