Reliability of numerical calculations. (Czech) Zbl 0879.65029

The paper is easy to read and surveys some basic points everybody involved in scientific computing should be aware of. The authors centre on the reliability of numerical results, and, via examples, present typical errors occurring in numerical computation. The devastating impact of roundoff error is illustrated by some incorrectly solved sensitive problems such as summation of an alternating series, numerical differentiation, eigenvalue calculation or a search for roots of the Wilkinson polynomial. Also, the use of improper methods and algorithms can lead to misleading, inaccurate, or even wrong results as the reader infers from examples based on Lagrange interpolation, numerical quadrature, and differential equations. Attention is payed to large scale computing, too. A comparison between Gaussian elimination and the conjugate gradient method is given. Finally, other sources of inaccuracy are mentioned and some conclusions drawn.
Reviewer: J.Chleboun (Praha)


65G50 Roundoff error
65D25 Numerical differentiation
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65B10 Numerical summation of series
65D32 Numerical quadrature and cubature formulas
65D05 Numerical interpolation
65F10 Iterative numerical methods for linear systems