TABLE OF CONTENTS The polynomial ( z ? 1) ( z - 2)...( z ? 20) is not a 'difficult' polynomial per se...
The 'difficulty' with the polynomial ? ( z ? i) is that of evaluating the explicit polynomial accurately. If on already knows the roots, then the polynomial can be evaluated without any loss of accuracy.
- J. H. WILKINSON, The Perfidious Polynomial (1984)
I first used backward error analysis in connection with simple programs for computing zeros of polynomials soon after the PILOT ACE came into use.
- J. H. WILKINSON, The State of the Art in Error Analysis (1985)
The Fundamental Theorem of Algebra asserts that every polynomial equation over the complex field has a root. It is almost beneath the dignity of such a majestic theorem to mention that in fact it has precisely n roots.
- J. H. WILKINSON, The Perfidious Polynomial (1984)
It can happen... that a particular polynomial can be evaluated accurately by nested multiplication, whereas evaluating the same polynomial by an economical method may produce relatively inaccurate results.
- C. T. FIKE, Computer Evaluation of Mathematical Functions (1968)
Two common tasks associated with polynomials are evaluation and interpolation: given the polynomial find its values at certain arguments, and given the values at certain arguments find the polynomial. We consider Horner's rule for evaluation and the Newton divided difference polynomial for interpolation. A third task not considered here is finding the zeros of a...
