Polynomial real root finding in Bernstein form

This dissertation presents pre-conditioning, isolation, and approximation concepts pertaining to finding the real roots of a polynomial in Bernstein form over a specified domain. Subdivision of a polynomial into smaller intervals prior to coefficient construction significantly improves the accuracy of the approximated roots as compared to "a posteriori" subdivision after the coefficients are generated. Real root isolation and approximation strategies are presented that exploit various properties of the Bernstein representation to compute the real roots of polynomials in Bernstein form. The numerical performance of these strategies is compared with other existing Bernstein and power form polynomial real root-finding strategies.

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