We investigate the parameter plane of the Newton’s method applied to the family of quartic polynomials pa,b(z) = z 4 +az + bz +az+ 1, where a and b are real parameters. We divide the parameter plane (a, b) ∈ R into twelve open and connected regions where p, p′ and p′′ have simple roots. In each of these regions we focus on the study of the Newton’s operator acting on the Riemann sphere.

Acknowledgement I would like to thank my mentor Prof. Dr. Krešimir Veseli´c for introducing me to the exciting field of relative error analysis, for devoting to me a lot of his time, and for sharing with me so many of his ideas. I also thank my colleagues Eberhard Pietzsch, Zlatko Drmač und Xiaofeng Wang for the possibility to check my ideas in numerous discussions, and Prof. his valuable and d...

The method used is a direct method based on a sparse variant of Gaussian elimination and is discussed further by Duff and Reid, ACM Trans. Math. Software 9 (1983), 302-325. A detailed discussion on the MA57 strategy and performance is given by Duff, ACM Trans. Math. Software 30 (2004), 118-144. Relevant work on pivoting and scaling strategies is given by Duff and Pralet, SIAM Journal Matrix Ana...

Virtualization is one of the biggest buzzwords of the technology industry right at this moment. The fast growth in storage capacity and processing power in enterprise installations coupled with the need for high availability, requires Storage Area Network (SAN) architecture to provide seamless addition of storage and performance elements without downtime. The usual goal of virtualization is to ...

The Q method of semidefinite programming, developed by Alizadeh, Haeberly and Overton, is extended to optimization problems over symmetric cones. At each iteration of the Q method, eigenvalues and Jordan frames of decision variables are updated using Newton’s method. We give an interior point and a pure Newton’s method based on the Q method. In another paper, the authors have shown that the Q m...

In this paper, the authors propose a new key generation algorithm based on using a binary image. The proposed algorithm converts 16×16 binary array representing the digital image into 4×4 array, then it converts the new generated array into 4×4 decimal array. The decimal array and the left diagonal of the original array are then used to generate the public key that is used to encrypt the data t...