The Conditions for the Convergence of Power Scaled Matrices and Applications

Xuzhou Chen, Robert E. Hartwig

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DOI: 10.4236/ajcm.2011.12007                

Abstract

For an invertible diagonal matrix D , the convergence of the power scaled matrix sequence D^-NA_N is investigated. As a special case, necessary and sufficient conditions are given for the convergence of D^-NT^N , where T is triangular. These conditions involve both the spectrum as well as the diagraph of the matrix .The results are then used to privide a new proof for the convergence of subspace iteration.

Keywords

Convergence, Iterative Method, Triangular matrix, Gram-Schmidt

Conflicts of Interest

The authors declare no conflicts of interest.

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