id: 06000262
dt: j
an: 2012a.00738
au: Cherif, Chokri; Goldstein, Avraham; Prado, Lucio M.G.
ti: Stability of linear equations ‒ algebraic approach.
so: Int. J. Math. Educ. Sci. Technol. 43, No. 1, 118-127 (2012).
py: 2012
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: N35 H65
ut: linear system; perturbed linear problems; stability; condition number
ci:
li: doi:10.1080/0020739X.2011.573870
ab: Summary: This article could be of interest to teachers of applied
mathematics as well as to people who are interested in applications of
linear algebra. We give a comprehensive study of linear systems from an
application point of view. Specifically, we give an overview of linear
systems and problems that can occur with the computed solution when the
coefficient matrix is obtained via experimentation. By giving the
initial tolerance for the solution, the estimate of the admissible
tolerance for the error matrix, and the error of the solution relative
to the norm of the computed solution can be determined. We use standard
properties of Banach algebra on matrices equipped with the spectral
norm.
rv: