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The Conditions for the Convergence of Power Scaled Matrices and Applications
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American Journal of Computational Mathematics·Volume 01 (2011)·Pages 63–71·Published 30 June 2011·DOI10.4236/ajcm.2011.12007
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Abstract
For an invertible diagonal matrix D , the convergence of the power scaled matrix sequence D<sup>-N</sup>A<sub>N</sub> is investigated. As a special case, necessary and sufficient conditions are given for the convergence of D<sup>-N</sup>T<sup>N</sup> , 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.
KeywordsConvergenceIterative MethodTriangular matrixGram-Schmidt
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