Numerical Approximation for Matrix Functions

ISBN-13: 9783659583933 / Angielski / Miękka / 2014 / 112 str.

El-Sayed Adel Abd Elaziz Abd Elhamid;Ramadan Mohamed a.

Opis

The matrix functions computations have an important area of research in numerical analysis for introducing numerical solutions of some types of differential equations and linear systems of equations. The main objective of this book, which consists of four chapters, is to introduce an analytical and numerical treatment for computing matrix functions based on five definitions of matrix functions for some types of matrices. Namely: matrix functions for square matrices having pure complex or mixed eigenvalues using Vandermonde matrix, Lagrange-Sylvester interpolation and mixed interpolation methods. Also for square matrices having mixed or repeated real eigenvalues using extension of Sylvesters definition and Newtons divided difference. The analytical analysis and numerical treatment of the proposed methods and techniques is studied. The accuracy of these proposed methods and techniques is demonstrated by several test problems where the obtained numerical results are compared with the exact values for some types of matrix functions and in other time compared with previous methods.

O autorze

Professor of Pure Mathematics, Head of Mathematics Department Faculty of Science , Menoufia University Adel Abd Elaziz Abd Elhamied El-sayed pursuing Ph.D. at the Department of Mathematics, The M.S. University of Fayoum University , Fayoum, He completed his post graduation from Fayoum University in the field of mathematics. His present areas of research are pure mathematics (numerical analysis).