Backward error and condition of structured linear systems. (English) Zbl 0747.65028

Higham, Desmond J.; Higham, Nicholas J.

SIAM J. Matrix Anal. Appl. 13, No. 1, 162-175 (1992).

Standard error concepts such as the normwise resp. componentwise backward error do not take into account the structure of linear systems except sparsity. To overcome this deficiency the authors introduce both the structured componentwise backward error related to the minimal \(\infty\)- norm solution to an underdetermined linear system and the structured condition number for which an explicit expression is derived. Applications including numerical results are given in case of symmetric matrices, Toeplitz matrices and the augmented system for least squares problems.

Reviewer: R.H.W.Hoppe (München)

MSC:

65F35	Numerical computation of matrix norms, conditioning, scaling
65F20	Numerical solutions to overdetermined systems, pseudoinverses
15A12	Conditioning of matrices
65G50	Roundoff error

Keywords:

structured componentwise backward error; underdetermined linear system; structured condition number; numerical results; symmetric matrices; Toeplitz matrices; least squares problems