Higher-order iterative methods for approximating zeros of analytic functions

AbstractIterative methods with extremely rapid convergence in floating-point arithmetic and circular arithmetic for simultaneously approximating simple zeros of analytic functions (inside a simple smooth closed contour in the complex plane) are presented. The R-order of convergence of the basic total-step and single-step methods, as well as their improvements which use Newton's and Halley's corrections, is given. Some hybrid algorithms that combine the efficiency of ordinary floating-point iterative methods with the accuracy control provided by interval arithmetic are also considered

Some improved inclusion methods for polynomial roots with Weierstrass' corrections

AbstractOne decade ago, the third order method without derivatives for the simultaneous inclusion of simple zeros of a polynomial was proposed in [1]. Following Nourein's idea [2], some modifications of this method with the increased convergence are proposed. The acceleration of convergence is attained by using Weierstrass' corrections without additional calculations, which provides a high computational efficiency of the modified methods. It is proved that their R-orders of convergence are asymptotically greater than 3.5. The presented interval methods are realized in circular complex arithmetic

Laguerre-like methods for the simultaneous approximation of polynomial multiple zeros

Two new methods of the fourth order for the simultaneous determination of multiple zeros of a polynomial are proposed. The presented methods are based on the fixed point relation of Laguerre's type and realized in ordinary complex arithmetic as well as circular complex interval arithmetic. The derived iterative formulas are suitable for the construction of modified methods with improved convergence rate with negligible additional operations. Very fast convergence of the considered methods is illustrated by two numerical examples

A new higher-order family of inclusion zero-finding methods

AbstractStarting from a suitable fixed point relation, a new one-parameter family of iterative methods for the simultaneous inclusion of complex zeros in circular complex arithmetic is constructed. It is proved that the order of convergence of this family is four. The convergence analysis is performed under computationally verifiable initial conditions. An approach for the construction of accelerated methods with negligible number of additional operations is discussed. To demonstrate convergence properties of the proposed family of methods, two numerical examples results are given

A Family of Three-Point Methods of Ostrowski's Type for Solving Nonlinear Equations

A class of three-point methods for solving nonlinear equations of eighth order is constructed. These methods are developed by combining two-point Ostrowski's fourth-order methods and a modified Newton's method in the third step, obtained by a suitable approximation of the first derivative using the product of three weight functions. The proposed three-step methods have order eight costing only four function evaluations, which supports the Kung-Traub conjecture on the optimal order of convergence. Two numerical examples for various weight functions are given to demonstrate very fast convergence and high computational efficiency of the proposed multipoint methods

Failure Analysis of the Tower Crane Counterjib

Failures of the cranes' structural parts unavoidably lead to serious damages or total collapses; these accidents are often followed by very high financial losses and possibly serious injuries or crane-related fatalities. The objective of this research was to identify the causes that led to the failure of the hammerhead tower crane (x1425C) counteijib. The crane is used for assembly works at the hydropower dam. The counteijib collapse resulted from a gusset plate failure and caused such significant damage of the whole crane structure that the crane was dismantled and removed from operation. The study of the accident includes: (1) Identification of the stress-state, where a FEM model is developed to provide a useful tool for studying stress analysis; (2) Laboratory investigations are conducted in order to define the chemical composition and mechanical properties of the material, the tensile properties, hardness, impact toughness, as well as the metallographic analyses. The analysis of the obtained results showed that the principal reasons behind the gusset plate failure originated from design and fabrication faults. The working stress was higher than the allowable one. Also, impact toughness was too low and the fabrication of welds was incorrect

Failure Analysis of the Tower Crane Counterjib

Failures of the cranes' structural parts unavoidably lead to serious damages or total collapses; these accidents are often followed by very high financial losses and possibly serious injuries or crane-related fatalities. The objective of this research was to identify the causes that led to the failure of the hammerhead tower crane (x1425C) counteijib. The crane is used for assembly works at the hydropower dam. The counteijib collapse resulted from a gusset plate failure and caused such significant damage of the whole crane structure that the crane was dismantled and removed from operation. The study of the accident includes: (1) Identification of the stress-state, where a FEM model is developed to provide a useful tool for studying stress analysis; (2) Laboratory investigations are conducted in order to define the chemical composition and mechanical properties of the material, the tensile properties, hardness, impact toughness, as well as the metallographic analyses. The analysis of the obtained results showed that the principal reasons behind the gusset plate failure originated from design and fabrication faults. The working stress was higher than the allowable one. Also, impact toughness was too low and the fabrication of welds was incorrect

Ultrasound Synthesis of Poly-DL-lactide-co-glycolide/Hydroxyapatite Core-shell Nano-spheres

Poster presented at the 8th World Biomaterials Congress, Amsterdam, The Netherlands, May 28 – June 1, 200

Buckets of the bucket wheel excavators: failures and redesign

Design of the buckets of the bucket wheel excavators has to meet the set of the functional requirements imposed by the processes of: (a) soil cutting; (b) filling; (c) transportation of the grabbed soil; (d) emptying. Optimal conduct of each of these processes imposes requirements, which are often in mutual collision. Except functional requirements, bucket structure has to meet, naturally, rigidity as well as strength criterion. During exploitation in harsh working conditions, failures of buckets occur relatively frequently. There are two basic types of bucket failures: structural and technological. In this paper, two bucket structural failures as well as one technological bucket failure are presented. Investigations' results pointed out that structural failures are caused by 'design-in' as well 'manufacturing-in' defects. Technological failure of the bucket was also of the 'design-in' type. Besides that, the redesigned buckets' are presented. Exploitation after the reconstruction fully confirmed the validity of the presented reconstruction design