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Rounding errors in numerical solutions of two linear equations in two unknowns
Author(s) -
Stummel F.,
Wendland W.
Publication year - 1982
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670040135
Subject(s) - rounding , mathematics , round off error , stability (learning theory) , gaussian elimination , numerical stability , gaussian , numerical analysis , mathematical analysis , computer science , operating system , physics , quantum mechanics , machine learning
Abstract New condition numbers and stability constants for the numerical behaviour of Cramer's rule and Gaussian elimination for solving two linear equations in two unknowns under data perturbations and rounding errors of floating‐point arithmetic are established. By these means fundamental error estimates and stability theorems are proved. The error estimates are illustrated by a series of numerical examples.