Chai Wah Wu
Linear Algebra and Its Applications
It is shown that if one uses a carefully defined concept of stability (Stewart, G.W., Introduction to matrix computations, Academic Press, New York and London, 1973) then Horner's rule for the evaluation of a polynomial and some other evaluation methods are not always stable. A method is presented which is always stable. The operations count for this method is the same as that for Horner's rule. The method is generalized to apply to all rational functions of one variable. © 1983 Springer-Verlag.
Chai Wah Wu
Linear Algebra and Its Applications
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ISIT 2007