TABLE OF CONTENTS A method of inverting the problem of round-off error is proposed which we plan to employ in other contexts and which suggests that it may be unwise to separate the estimation of round-off error from that due to observation and truncation.
- WALLACE J. GIVENS, Numerical Computation of the Characteristic Values of a Real Symmetric Matrix (1954)
The enjoyment of one's tools is an essential ingredient of successful work.
- DONALD E. KNUTH, The Art of Computer Programming, Volume 2, Seminumerical Algorithms (1998)
The subject of propagation of rounding error, while of undisputed importance in numerical analysis, is notorious for the difficulties which it presents when it is to be taught in the classroom in such a manner that the student is neither insulted by lack of mathematical content nor bored by lack of transparence and clarity.
- PETER HENRICI, A Model for the Propagation of Rounding Error in Floating Arithmetic (1980)
The two main classes of rounding error analysis are not, as my audience might imagine, 'backwards' and 'forwards', but rather 'one's own' and 'other people's'. One's own is, of course, a model of lucidity; that of others serves only to obscure the essential simplicity of the matter in hand.
- J. H. WILKINSON, The State of the Art in Error Analysis (1985)
Having defined a model for floating point arithmetic in the last chapter, we now apply the model to some basic matrix computations, beginning with inner products. This first application...
