We present methods for computing the generalized polar decomposition of a matrix based on dynamically weighted Halley iteration. This method is well established standard decomposition. A stable implementation available, where inversion avoided and QR decompositions are used instead. establish natural generalization this approach with respect to signature matrices. Again inverse can be by using ...

In a recent paper, Noor [M. Aslam Noor, New classes of iterative methods for nonlinear equations, Appl. Math. Comput., 2007, doi:10.1016/j.amc:2007], suggested and analyzed a generalized one parameter Halley method for solving nonlinear equations using. In this paper, we modified this method which has fourth order convergence. As special cases, we obtain a family of third-order iterative method...

Comet 1P/Halley has the unique distinction of having a very comprehensive set of observational records for almost every perihelion passage from 240 B.C. This has helped to constrain theoretical models pertaining to its orbital evolution. Many previous works have shown the active role of mean motion resonances in the evolution of various meteoroid streams. Here we look at how various resonances,...

Solving a quadratic equation P (x) = ax + bx+ c = 0 with real coefficients is known to middle school students. Solving the equation over the quaternions is not straightforward. Huang and So [2] give a complete set of formulas, breaking it into several cases depending on the coefficients. From a result of the second author in [10], zeros of P (x) can be expressed in terms of the zeros of a real ...

S. Z. Khalaf, A. A. Selman and E. E. Abd_Al lattef Abstract— The physical properties of the interaction region between the solar wind and Halley comet have been taken a considerable atten-tion in this work. The cometary ion tail that formed and shaped by the existence of the interplanetary magnetic field (IMF) is also depends on the comet type. This interaction can be described by plasma and ma...

This paper is dedicated to the study of continuous Newton’s method, which is a generic differential equation whose associated flow tends to the zeros of a given polynomial. Firstly, we analyze some numerical features related to the root-finding methods obtained after applying different numerical methods for solving initial value problems. The relationship between the step size and the order of ...

Recent advances in techniques of critical close reading historical texts can now be applied to records pre-telescopic celestial observations - allowing significant progress for analyzing and solving orbits past comets: we exemplify our method by the orbit comet AD 760 only with then identify it 1P/Halley. A detailed eyewitness record drawing a Syriac Chronicle Zuqnin (finished 775/6) was not ye...