Lecture 4

Eugene E. Tyrtyshnikov
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Eugene E. Tyrtyshnikov: Russian Academy of Sciences, Institute of Numerical Mathematics

A chapter in A Brief Introduction to Numerical Analysis, 1997, pp 31-37 from Springer

Abstract: Abstract A matrix A ∈ ℂ n×n is row-wise diagonally dominant if (4.1.1) $$ |a_{ii} | > r_i \equiv \sum\limits_{\begin{array}{*{20}c} {j = 1} \\ {j \ne i} \\ \end{array} }^n {|a_{ij} |, i = 1,...,n,} $$ and column-wise diagonally dominant if (4.1.2) $$ |a_{jj} | > c_j \equiv \sum\limits_{\begin{array}{*{20}c} {i = 1} \\ {i \ne j} \\ \end{array} }^n {|a_{ij} |, j = 1,...,n.} $$

Keywords: Condition Number; Analytic Perturbation; Simple Eigenvalue; Lower Triangular Matrix; Multiple Eigenvalue (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1007/978-0-8176-8136-4_4

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