alexa Backward Error and Condition of Structured Linear Systems Read More: http: epubs.siam.org doi abs 10.1137 0613014
Mathematics

Mathematics

Journal of Physical Mathematics

Author(s): Higham DJ, Nicholas J Higham

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Existing definitions of backward error and condition number for linear systems do not cater to structure in the coefficient matrix, except possibly for sparsity. The definitions are extended so that when the coefficient matrix has structure the perturbed matrix has this structure too. It is shown that when the structure comprises linear dependence on a set of parameters, the structured componentwise backward error is given by the solution of minimal $\infty $ -norm to an underdetermined linear system; an explicit expression for the condition number in this linear case is also obtained. Applications to symmetric matrices, Toeplitz matrices and the least squares problem are discussed and illustrated through numerical examples. Read More: http://epubs.siam.org/doi/abs/10.1137/0613014

This article was published in SIAM. J. Matrix Anal. & Appl. and referenced in Journal of Physical Mathematics

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