Inverse Family of Numerical Methods for Approximating All Simple and Roots with Multiplicity of Nonlinear Polynomial Equations with Engineering Applications

A new inverse family of the iterative method is interrogated in the present article for simultaneously estimating all distinct and multiple roots of nonlinear polynomial equations. Convergence analysis proves that the order of convergence of the newly constructed family of methods is two. The computer algebra systems CAS-Mathematica is used to determine the lower bound of convergence order, which justifies the local convergence of the newly developed method. Some nonlinear models from physics, chemistry, and engineering sciences are considered to demonstrate the performance and efficiency of the newly constructed family of inverse simultaneous methods in comparison to classical methods in the literature. The computational time in seconds and residual error graph of the inverse simultaneous methods are also presented to elaborate their convergence behavior.

Efficient iterative methods for finding simultaneously all the multiple roots of polynomial equation

Two new iterative methods for the simultaneous determination of all multiple as well as distinct roots of nonlinear polynomial equation are established, using two suitable corrections to achieve a very high computational efficiency as compared to the existing methods in the literature. Convergence analysis shows that the orders of convergence of the newly constructed simultaneous methods are 10 and 12. At the end, numerical test examples are given to check the efficiency and numerical performance of these simultaneous methods.

Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications

We introduce here a new two-step derivate-free inverse simultaneous iterative method for estimating all roots of nonlinear equation. It is proved that convergence order of the newly constructed method is four. Lower bound of the convergence order is determined using Mathematica and verified with theoretical local convergence order of the method introduced. Some nonlinear models which are taken from physical and engineering sciences as numerical test examples to demonstrate the performance and efficiency of the newly constructed modified inverse simultaneous methods as compared to classical methods existing in literature are presented. Dynamical planes and residual graphs are drawn using MATLAB to elaborate efficiency, robustness, and authentication in its domain.

Perbandingan Pergerakan Titik Pantau Deformasi Kepulauan Sangihe Menggunakan Metode Perhitungan Periodik dan Simultan Berdasarkan Data GNSS Tahun 2014, 2015, dan 2016

The study of deformation monitoring point movement of Sangihe Islands was conducted using the GNSS measurement methods. One of the factor that determines the accuracy of the deformation monitoring is the utilized data processing methods. Therefore, this research analyze the comparison of deformation monitoring point movement of Sangihe Islands using periodic and simultaneous GNSS data processing methods. This research used three observations epochs of GNSS, i.e. 2014, 2015 and 2016. The observational data were processed using GAMIT/GLOBK software that tied to ITRF 2014 to produce coordinates and their accuracy. Based on the coordinate data and its accuracy, the velocity of movements calculation and their accuracy was done using the periodic and simultaneous methods. Based on the periodic method, the velocity of the SGH1 point on the N component is -1,11 ± 2,72 mm/year, on the E component is 9,21 ± 4,17 mm/year, and on the U component is -15,02 ± 50,64 mm/year, while the velocity of the SGH3 point on the N component is -4,93 ± 1,56 mm/year, on the E component is 16,50 ± 2,47 mm/year, and on the U component is -6,69 ± 19,42 mm/year. Based on the simultaneous method, the velocity of the SGH1 point on the N component is -1,56 ± 1,25 mm/year, on the E component is 9,40 ± 1,55 mm/year, and on the U component is -11,54 ± 5,83 mm/year, while the velocity of the SGH3 point on the N component is -5,18 ± 0,88 mm/year, on the E component is 16,91 ± 1,10 mm/year, and on the U component is -2,84 ± 3,49 mm/year. This research proves the hypothesis that the simultaneous GNSS data calculation results in higher accuracy than the periodic method.

Concurrent Defects, Methodologies and Recommendations

Software testing is a major process in every software development cycle so as to produce superior quality products that can cater to the customer needs. In the beginning of the IT industry testing was a simple process since competition was not enough so as to produce good quality software. With the development of technology and fierce competition over recent years the needs to develop simultaneous methods of testing have been proposed. Reviewing the given application remains one of the major setbacks of concurrent code and the other being data flow in given request stack. Testing becomes really difficult when the function not returning the output to the caller function in requisite time but later on returns it via call-back functions, messages or other such processes. So this paper aims at viewing the tools and techniques available for better testing, removing bugs so as to make software good. Here the defects as well as directions need to remove it are also focussed.

Computer tools for the construction and analysis of some efficient root-finding simultaneous methods

Using the tools provided by computer algebra system Mathematica, we consider two iterative methods of high efficiency for the simultaneous approximation of simple or multiple (real or complex) zeros of algebraic polynomials. The proposed methods are based on the fourth-order Schr?der-like methods of the first and second kind. We prove that the order of convergence of both basic total-step simultaneous methods is equal to five. Using corrective approximations produced by methods of order two, three and four for finding a single multiple zero, the convergence order is increased from five to six, seven, and eight, respectively. The increased convergence speed is attained with negligible number of additional arithmetic operations, which significantly increases the computational efficiency of the accelerated methods. Convergence properties of the proposed methods are demonstrated by numerical examples and graphics visualization by plotting trajectories of zero approximations. Flows of iterative processes, presented by these trajectories, point to the stability and robustness of the proposed methods.

Test–Retest Reliability of Cervical and Ocular Vestibular Evoked Myogenic Potential With Simultaneous and Sequential Recording

Purpose Simultaneous recording of cervical (cVEMP) and ocular (oVEMP) vestibular evoked myogenic potentials aids in reducing the testing time when compared to conventional sequential recordings. The purpose of this study was to examine the test–retest reliability of sequential and simultaneous acquisitions of cVEMP and oVEMP. Method cVEMP and oVEMP were recorded in 35 normal-hearing individuals. The cVEMP and oVEMP were obtained using sequential and simultaneous methods. The VEMP recordings were performed across 3 sessions. The 1st 2 recording sessions were consecutive with a gap of 5 min between sessions. The 3rd recording session was after a gap of 3–5 days. Results Both simultaneous and sequential recordings showed fair-to-good test–retest reliability for latencies and amplitude of cVEMP and oVEMP. Conclusion Simultaneous cVEMP and oVEMP recordings can be used to obtain fast VEMP recording with test–retest reliability comparable with that of sequential recording.