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Structured Backward Error and Condition Number for Linear Systems of the Type A* Ax = b |
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| Authors: | V Frayssé S Gratton V Toumazou |
| Institution: | (1) CERFACS, 42 avenue Gaspard Coriolis, 31057 Toulouse cedex 01, France.;(2) DTS/MPI/MS/MO, CNES, 18 avenue Edouard Belin, 31401 Toulouse cedex 04, France.;(3) LEGOS-GRGS / CNES, 18 avenue Edouard Belin, 31401 Toulouse cedex 04, France. |
| Abstract: | We present a formulation for the structured condition number and for the structured backward error for the linear system A* Ax = b, when the rectangular matrix A is subjected to normwise perturbations. Perturbations on the data A and the solution x are measured in the Frobenius norm. Numerical experiments are provided that show the relevance of this condition number in the prediction of the computing error when solving such systems. |
| Keywords: | Structured perturbations condition number backward error linear systems |
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