Iterative Algorithms For Producing The Optimally Scaled Matrix, Computing The Spectral Radius Of The Jacobi Iterative Matrix, Bounding ‖A～(-1)‖_∞ And Judging M-matrices

Iterative algorithms for calculating bounds of ∥A^-1∥_∞and the spectralradius of the Jacobi iterative matrix, judging H-matrix and M-matrix andproducing the optimally scaled matrix and equidiagonal dominance matrix arepresented in this paper.In Chapter 2, an new iterative algorithm for judging H-matrix ispresented. We also analyze the convergence of the new iterative algorithm.Numerical test results are presented. The results show that the new algorithmis better than other iterative algorithm that was introduced in this chapter.In Chapter 3, we propose a new iterative algorithm for producing theoptimally scaled matrix and calculating the spectral of the Jacobi iterativematrix. Also, by the algorithm, one can easily judge whether a matrix anH-matrix (or a M-matrix) or not. The convergence of the algorithm wasproofed and several numerical test results are presented.In Chapter 4, an iterative algorithm for estimating ∥A^-1∥_∞and producingthe equidiagonal dominance matrix is presented, and the algorithm presentedis also an algorithm for judging M-matrices and H-matrix. The convergence ofthe algorithm was proofed and several numerical test results are presented inthis chapter.