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Discrete mathematical models in the analysis of splitting iterative methods for linear systems

✍ Scribed by Begoña Cantó; Carmen Coll; Elena Sánchez

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
231 KB
Volume
56
Category
Article
ISSN
0898-1221

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✦ Synopsis

Splitting methods are used to solve most of the linear systems, Ax = b, when the conventional method of Gauss is not efficient. These methods use the factorization of the square matrix A into two matrices M and N as A = M -N where M is nonsingular. Basic iterative methods such as Jacobi or Gauss-Seidel define the iterative scheme for matrices that have no zeros along its main diagonal.

This paper is concerned with the development of an iterative method to approximate solutions when the coefficient matrix A has some zero diagonal entries. The algorithm developed in this paper involves the analysis of a discrete-time descriptor system given by the equation Me(k + 1) = N e(k), e(k) being the error vector.

📜 SIMILAR VOLUMES

Note to the mixed-type splitting iterati
Note to the mixed-type splitting iterative method for Z-matrices linear systems
✍ Guang-Hui Cheng; Ting-Zhu Huang; Shu-Qian Shen 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 136 KB

In this paper, the mixed-type splitting iterative method is established for solving the linear system Ax = b, where A is a Z-matrix. The iterative method contains an auxiliary matrix L 1 (D 1 ) that is restricted to be nonnegative strictly lower triangular (diagonal) matrix. Comparison theorems show