Speaker
Aaron Melman
(Santa Clara University)
Description
Useful properties of scalar polynomials can be obtained by embedding them into the larger framework of their generalization to matrix polynomials. As an example of this, we derive explicit simple upper bounds on the magnitudes of scalar polynomial zeros that are close approximations of the Cauchy radius. Their complexity is of the order of a single polynomial evaluation.
The Cauchy radius is an upper bound that is optimal among all bounds depending only on the moduli of the coefficients, but it has the disadvantage of requiring the solution of a nonlinear equation, so that the close explicit approximation we obtain is a useful substitute.
Primary author
Aaron Melman
(Santa Clara University)
