Chapter 50
Vector and Matrix Norms, Error Analysis, Efficiency, and Stability
Ralph Byers
University of Kansas
Biswa Nath Datta
Northern Illinois University
Calculations are subject to errors. There may be modeling errors, measurement errors, manufacturing errors, noise, equipment is subject to wear and damage, etc. In preparation for computation, data must often be perturbed by rounding it to fit a particular finite precision, floating-point format. Further errors may be introduced during a computation by using finite precision arithmetic and by truncating an infinite process down to a finite number of steps.
This chapter outlines aspects of how such errors affect the results of a mathematical computation with an emphasis on matrix computations. ...
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