Document Details

Document Type : Thesis 
Document Title :
Efficient novel iterative methods for nonlinear problems and matrix functions
طرق تكرارية جديدة فعالة للمسائل غير الخطية ودوال المصفوفات
 
Subject : Faculty of Science 
Document Language : Arabic 
Abstract : Iterative methods play curial roles everywhere in mathematics. Especially, when it comes to practical problems, their solving processes are mostly led to iteration schemes, in which an iterative process should be used for converging to the true solution by considering appropriate conditions on the choice of the input data. Here, we develop two numerical iterative schemes. In the first scheme, it is investigated on an iterative scheme to calculate the matrix square root and its inversion simultaneously. It is constructed via the concept of matrix sign function. Convergence properties are discussed under some conditions on the choice of the initial matrix as well as the input matrix A. It is then attempted to propose an iterative method possessing higher convergence order, which is also stable. Extension of the proposed scheme to the pth root of a matrix is also given. Ultimately, several tests including an application of the proposed iterative method to solve matrix differential equations is brought forward. In the second scheme, a new scheme is proposed under the umbrella of iteration methods to compute the sign of an invertible matrix. To this target, a review of the exiting solvers of the same type is given and then a new scheme is derived based on a multi-step Newton-type nonlinear equation solver. It is shown that the new method and its reciprocal converge glob ally with wider convergence radii in contrast to their competitors of the same order from the general Pade schemes. After investigation on the theoretical parts, numerical experiments ´ based on complex matrices of various sizes are furnished to reveal the superiority of the proposed solver in terms of the elapse CPU time. 
Supervisor : Dr. Malik Zaka Ullah 
Thesis Type : Master Thesis 
Publishing Year : 1445 AH
2023 AD 
Co-Supervisor : Dr. Fouad Othman Mallawi 
Added Date : Wednesday, December 27, 2023 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
سلطان معيش العصلانيAlaslani, Sultan MuayshResearcherMaster 

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