Root neighborhoods of a polynomial

Author:
Ronald G. Mosier

Journal:
Math. Comp. **47** (1986), 265-273

MSC:
Primary 65G05; Secondary 12D10, 30C10, 30C15

DOI:
https://doi.org/10.1090/S0025-5718-1986-0842134-4

MathSciNet review:
842134

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Abstract: The root neighborhoods of , a polynomial over the complex field, are the sets of complex numbers that are the roots of polynomials which are near to . The term 'near' means that the coefficients of the polynomials are within some fixed magnitude of the coefficients of . A necessary and sufficient condition for a complex number to be in the root neighborhoods is given and it is proved that each root neighborhood contains at least one root of and the same number of roots of each near polynomial. Finally, a necessary and sufficient condition is given for a root neighborhood to contain more than one root of , and consequently more than one root of any of the near polynomials.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0842134-4

Article copyright:
© Copyright 1986
American Mathematical Society